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On variable-order fractional linear viscoelasticity Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-13 Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli
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Well-posedness and stability of a fractional heat-conductor with fading memory Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-10 Sebti Kerbal, Nasser-eddine Tatar, Nasser Al-Salti
We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler
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Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-10 Neha Gupta, Arun Kumar, Nikolai Leonenko, Jayme Vaz
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Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-06 Xuan X. Xi, Yong Zhou, Mimi Hou
In this paper, we study a class of backward problems for nonlinear fractional super-diffusion equations in Banach spaces. We consider the time fractional derivative in the sense of Caputo type. First, we establish some results for the existence of the mild solutions. Moreover, we obtain regularity results of the first order and fractional derivatives of mild solutions. These conclusions are mainly
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On the convergence of the Galerkin method for random fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-06 Marc Jornet
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Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-03 Lihong Zhang, Xiaofeng Nie
In this paper, we prove Hopf’s lemma for the Logarithmic Laplacian. At first, we introduce the strong minimum principle. Then Hopf’s lemma for the Logarithmic Laplacian in the ball is proved. On this basis, Hopf’s lemma of the Logarithmic Laplacian is extended to any open set with the property of the interior ball. Finally, an example is given to explain Hopf’s lemma can be applied to the study of
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Non-confluence of fractional stochastic differential equations driven by Lévy process Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-03 Zhi Li, Tianquan Feng, Liping Xu
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Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-29 Emilia Bazhlekova
An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, \(\alpha \) and \(\alpha _m\), it is assumed \(1<\alpha <2\) and \(\alpha -\alpha _m\le 1\). Subordination principle with respect to the corresponding single-term time-fractional wave equation of
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Monotone iterative technique for multi-term time fractional measure differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-17 Haide Gou, Min Shi
In this paper, we investigate the existence and uniqueness of the S-asymptotically \(\omega \)-periodic mild solutions to a class of multi-term time-fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of S-asymptotically \(\omega \)-periodic mild solution to our concern problem, by means of Laplace transform and \((\beta
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A tempered subdiffusive Black–Scholes model Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-09 Grzegorz Krzyżanowski, Marcin Magdziarz
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Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-09 Lihong Zhang, Qi Liu, Bashir Ahmad, Guotao Wang
This paper studies the following coupled k-Hessian system with different order fractional Laplacian operators: $$\begin{aligned} {\left\{ \begin{array}{ll} {S_k}({D^2}w(x))-A(x)(-\varDelta )^{\alpha /2}w(x)=f(z(x)),\\ {S_k}({D^2}z(x))-B(x)(-\varDelta )^{\beta /2}z(x)=g(w(x)). \end{array}\right. } \end{aligned}$$ Firstly, we discuss decay at infinity principle and narrow region principle for the k-Hessian
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Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-08 Naqash Sarfraz, Muhammad Aslam, Qasim Ali Malik
In this paper, we define the \(p\)-adic mixed Morrey type spaces and study the boundedness of \(p\)-adic fractional integral operators and their commutators on these spaces. More precisely, we first obtain the boundedness of \(p\)-adic fractional integral operators and their commutators on \(p\)-adic mixed central Morrey spaces. Moreover, we further extend these results on \(p\)-adic generalized mixed
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Subordination results for a class of multi-term fractional Jeffreys-type equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-04 Emilia Bazhlekova
Jeffreys equation and its fractional generalizations provide extensions of the classical diffusive laws of Fourier and Fick for heat and particle transport. In this work, a class of multi-term time-fractional generalizations of the classical Jeffreys equation is studied. Restrictions on the parameters are derived, which ensure that the fundamental solution to the one-dimensional Cauchy problem is a
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Collage theorems, invertibility and fractal functions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-03 María A. Navascués, Ram N. Mohapatra
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Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Hengameh Tamimi, Somayeh Saiedinezhad, Mohammad Bagher Ghaemi
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Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Jinyi Sun, Chunlan Liu, Minghua Yang
The paper is concerned with the three-dimensional Boussinesq-Coriolis equations with Caputo time-fractional derivatives. Specifically, by striking new balances between the dispersion effects of the Coriolis force and the smoothing effects of the Laplacian dissipation involving with a time-fractional evolution mechanism, we obtain the global existence of mild solutions to Cauchy problem of three-dimensional
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Transformations of the matrices of the fractional linear systems to their canonical stable forms Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Tadeusz Kaczorek, Lukasz Sajewski
A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the existence of the solution to the transformation problem of the linear system to its asymptotically stable controllable and observable canonical forms with desired eigenvalues are given and illustrated by numerical examples of fractional linear systems.
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Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Armen M. Jerbashian, Spartak G. Rafayelyan, Joel E. Restrepo
This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3, 4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for functions
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Relative controllability of linear state-delay fractional systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25 Nazim I. Mahmudov
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Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25 Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy
In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type (\(\theta \)-type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that \(\theta \in (\frac{1}{2},1)\), which remains untreated in the literature. The proposed
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-22 Jacky Cresson, Anna Szafrańska
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Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$ Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Truong Vinh An, Vasile Lupulescu, Ngo Van Hoa
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Rich phenomenology of the solutions in a fractional Duffing equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Sara Hamaizia, Salvador Jiménez, M. Pilar Velasco
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Sum of series and new relations for Mittag-Leffler functions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-19 Sarah A. Deif, E. Capelas de Oliveira
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11 Hassan Askari, Alireza Ansari
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Global optimization of a nonlinear system of differential equations involving $$\psi $$ -Hilfer fractional derivatives of complex order Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11 Pradip Ramesh Patle, Moosa Gabeleh, Vladimir Rakočević
In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential
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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-05 Pawan Kumar Mishra, Vinayak Mani Tripathi
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Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-04 Nikola Kosturski, Svetozar Margenov
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Analysis of a class of completely non-local elliptic diffusion operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-29 Yulong Li, Emine Çelik, Aleksey S. Telyakovskiy
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Discrete convolution operators and equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Rui A. C. Ferreira, César D. A. Rocha
In this work we introduce discrete convolution operators and study their most basic properties. We then solve linear difference equations depending on such operators. The theory herein developed generalizes, in particular, the theory of discrete fractional calculus and fractional difference equations. To that matter we make use of the so-called Sonine pairs of kernels.
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Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Zuomao Yan
We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of \(\alpha \)-order sine and cosine family and Picard type approximate sequences, we
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Optimal control of fractional non-autonomous evolution inclusions with Clarke subdifferential Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Xuemei Li, Xinge Liu, Fengzhen Long
In this paper, the non-autonomous fractional evolution inclusions of Clarke subdifferential type in a separable reflexive Banach space are investigated. The mild solution of the non-autonomous fractional evolution inclusions of Clarke subdifferential type is defined by introducing the operators \(\psi (t,\tau )\) and \(\phi (t,\tau )\) and V(t), which are generated by the operator \(-\mathcal {A}(t)\)
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A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26 C. L. Frota, M. A. Jorge Silva, S. B. Pinheiro
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Schrödinger-Maxwell equations driven by mixed local-nonlocal operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26 Nicolò Cangiotti, Maicol Caponi, Alberto Maione, Enzo Vitillaro
In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then
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The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26 Paulo Mendes Carvalho Neto, Renato Fehlberg Júnior
In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\), with \(1\le q\le p/(1-p\alpha )\), whether \(I=[t_0,t_1]\) or \(I=[t_0,\infty )\) and X is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from \(L^p(t_0
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Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz
Let \(0
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Operational matrix based numerical scheme for the solution of time fractional diffusion equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 S. Poojitha, Ashish Awasthi
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Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Ravshan Ashurov, Rajapboy Saparbayev
This study investigates the inverse problem of determining the right-hand side of a telegraph equation given in a Hilbert space. The main equation under consideration has the form \((D_{t}^{\rho })^{2}u(t)+2\alpha D_{t}^{\rho }u(t)+Au(t)=p( t)q+f(t)\), where \(0
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Generalized Krätzel functions: an analytic study Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Ashik A. Kabeer, Dilip Kumar
The paper is devoted to the study of generalized Krätzel functions, which are the kernel functions of type-1 and type-2 pathway transforms. Various analytical properties such as Lipschitz continuity, fixed point property and integrability of these functions are investigated. Furthermore, the paper introduces two new inequalities associated with generalized Krätzel functions. The composition formulae
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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan D. Repovš
We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there
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Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Zhiqiang Li, Yubin Yan
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the \(\psi \)-Caputo derivative of order \(\alpha \in (0,1)\) and the spectral fractional Laplacian of order \(\beta \in (\frac{1}{2},1]\). The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the
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Asymptotic behavior for a porous-elastic system with fractional derivative-type internal dissipation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Wilson Oliveira, Sebastião Cordeiro, Carlos Alberto Raposo da Cunha, Octavio Vera
This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem
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Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-20 Qiang Li, Jina Zhao, Mei Wei
The purpose of this paper is to consider the fractional delayed evolution equation of order \(\gamma \in (1,2)\) in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear function
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Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16 Rachid Echarghaoui, Moussa Khouakhi, Mohamed Masmodi
In this paper, we consider the following problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\varDelta )^{s} u=g(x) u^{2_{s}^{*}-1}+\lambda u^{-\gamma }, &{} \text { in } \varOmega , \\ u>0, \text { in } \varOmega , \quad u=0, &{} \text { on } \partial \varOmega , \end{array}\right. } \end{aligned}$$ where \(\varOmega \subset {\mathbb {R}}^{N}(N > 2s)\) is a smooth bounded domain, \(s\in (0,1)\)
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Some boundedness results for Riemann-Liouville tempered fractional integrals Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16 César E. Torres Ledesma, Hernán A. Cuti Gutierrez, Jesús P. Avalos Rodríguez, Willy Zubiaga Vera
In this work we generalize some results of the Riemann-Liouville fractional calculus for the tempered case, namely, we deal with some boundedness results of Riemann-Liouville tempered fractional integrals on continuous function space and Lebesgue spaces in bounded intervals and on the real line. Moreover, the limit behavior of the Riemann-Liouville tempered fractional integrals approaching to the Riemann-Liouville
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Representations of solutions of systems of time-fractional pseudo-differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16 Sabir Umarov
Systems of fractional order differential and pseudo-differential equations are used in modeling of various dynamical processes. In the analysis of such models, including stability analysis, asymptotic behaviors, etc., it is useful to have a representation formulas for the solution. In this paper we prove the existence and uniqueness theorems and derive representation formulas for the solution of general
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-14 K. S. Vishnukumar, M. Vellappandi, V. Govindaraj
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Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-25 Yu He, Qi Sun, Ciqiang Zhuo
Let \(p(\cdot ),\ q(\cdot )\) and \(\alpha (\cdot )\) be variable exponents satisfying some Hölder continuous conditions. In this paper, the authors characterize the variable inhomogeneous Besov space \(B_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}(\mathbb {R}^n)\) and the variable inhomogeneous Triebel-Lizorkin space \(F_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}(\mathbb {R}^n)\) in terms of Hajłasz gradient
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Log-concavity and log-convexity of series containing multiple Pochhammer symbols Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-22 Dmitrii Karp, Yi Zhang
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated. We show that logarithmic concavity (convexity) of the generic sequence leads to logarithmic concavity (convexity) of the sum of the series with respect to the argument
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Decay estimates and extinction properties for some parabolic equations with fractional time derivatives Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-16 Tahir Boudjeriou
The main goal of this paper is to study the asymptotic behaviour and the finite extinction time of weak solutions to some time-fractional parabolic equations. Moreover, we improve some results in [5, 10] by dropping out some conditions assumed there.
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Lump solutions of the fractional Kadomtsev–Petviashvili equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-10 Handan Borluk, Gabriele Bruell, Dag Nilsson
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A mutually exciting rough jump-diffusion for financial modelling Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-02 Donatien Hainaut
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On some even-sequential fractional boundary-value problems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-02 Ekin Uğurlu
In this paper we provide a way to handle some symmetric fractional boundary-value problems. Indeed, first, we consider some system of fractional equations. We introduce the existence and uniqueness of solutions of the systems of equations and we show that they are entire functions of the spectral parameter. In particular, we show that the solutions are at most of order 1/2. Moreover we share the integration
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Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-29 Takwon Kim, Jinwan Park, Ji-Hun Yoon, Ki-Ahm Lee
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Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-22
Abstract As a follow-up to the inherent nature of Caputo-Hadamard fractional derivative (CHFD) and the Hadamard fractional derivative ( HFD), little is known about some asymptotic behaviors of solutions. In this paper, a system of fractional differential equations including two types of fractional derivatives the CHFD and the HFD is investigated. The leading derivative is of an order between zero and
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On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-21 Jacek Sadowski
The purpose of this text is to propose an attempt of an extension of the Filippov-Ważewski Relaxation Theorem for a certain class of fractional differential inclusions. The classical result devoted to ordinary differential inclusions is a part of the qualitative theory: a description of the relationship between the solutions to the differential inclusion and the convexified differential inclusion was
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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-20 Anatoly A. Alikhanov, Mohammad Shahbazi Asl, Chengming Huang
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the development of a numerical method and analysis, the original problem is transformed into a new integro-differential model which includes the Caputo derivatives and the Riemann-Liouville fractional integrals with orders belonging
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Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-20
Abstract A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg equation with a Caputo time derivative of order \(\alpha \in (0,1)\) . The variable-step L1 formula and the finite difference method are employed for the time and the space discretizations, respectively. The unique solvability of the numerical scheme is proved by the Brouwer fixed-point theorem
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A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-06 Zhao Jing, Zhenhai Liu, Nikolaos S. Papageorgiou
The main purpose of this paper is to study an abstract system which consists of a parabolic hemivariational inequality with a Hilfer fractional evolution equation involving history-dependent operators, which is called a Hilfer fractional differential hemivariational inequality. We first show existence and a priori estimates for the parabolic hemivariational inequality. Then, by using the well-known
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Robust model predictive control for fractional-order descriptor systems with uncertainty Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-01 Adnène Arbi
In this study, a new robust predictive control technique is investigated for uncertain fractional-order descriptor systems. Using the properties of fractional calculus and the construction of an appropriate Lyapunov function, the sufficient conditions to guarantee the existence of a robust predictive controller are given by minimizing the worst-case optimization problem. The new robust predictive controller