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Short time coupled fractional fourier transform and the uncertainty principle Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Ramanathan Kamalakkannan, Rajakumar Roopkumar, Ahmed ZayedIn this paper, we introduce a shorttime coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft ). We then prove that it satisfies Parseval’s relation, derive its inversion and addition formulas, and characterize its range on ℒ 2 (ℝ 2 ). We also study its time delay and frequency shift properties and conclude the article by a derivation

Sharp asymptotics in a fractional SturmLiouville problem Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Pavel Chigansky, Marina KleptsynaThe current research of fractional SturmLiouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a different route, namely, construction of explicit asymptotic approximations for the solutions. As a study case, we consider a problem with left and right RiemannLiouville

Approximate calculation of the Caputotype fractional derivative from inaccurate data. Dynamical approach Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Platon G. SurkovA specific formulation of the “classical” problem of mathematical analysis is considered. This is the problem of calculating the derivative of a function. The purpose of this work is to construct an algorithm for the approximate calculation of the Caputotype fractional derivative based on the methods of control theory. The input data of the algorithm is represented by inaccurate measured function

Sliding methods for the higher order fractional laplacians Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Leyun WuIn this paper, we develop a sliding method for the higher order fractional Laplacians. We first obtain the key ingredients to obtain monotonicity of solutions, such as narrow region maximum principles in bounded or unbounded domains. Then we introduce a new idea of estimating the singular integrals defining the fractional Laplacian along a sequence of approximate maximum points and illustrate how this

Frontmatter Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Article Frontmatter was published on June 1, 2021 in the journal Fractional Calculus and Applied Analysis (volume 24, issue 3).

In memory of the honorary founding editors behind the FCAA success story Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Virginia Kiryakova, J.A. Tenreiro Machado, Yuri LuchkoIn this editorial paper, we start by surveying of the main milestones in the organization, foundation, and development of the journal Fractional Calculus and Applied Analysis ( FCAA ). The main potential of FCAA is in its readers, authors, and editors who contribute to the scientific advance and promote the progress of the journal. Among the editors, a special role of the honorary editors who contributed

(N + α)Order lowpass and highpass filter transfer functions for noncascade implementations approximating butterworth response Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
David Kubanek, Jaroslav Koton, Jan Jerabek, Darius AndriukaitisThe formula of the allpole lowpass frequency filter transfer function of the fractional order ( N + α ) designated for implementation by noncascade multiplefeedback analogue structures is presented. The aim is to determine the coefficients of this transfer function and its possible variants depending on the filter order and the distribution of the fractionalorder terms in the transfer function

Multiterm fractional integrodifferential equations in power growth function spaces Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Vu Kim Tuan, Dinh Thanh Duc, Tran Dinh PhungIn this paper we characterize the Laplace transform of functions with power growth square averages and study several multiterm Caputo and RiemannLiouville fractional integrodifferential equations in this space of functions.

Galerkin method for time fractional semilinear equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Yamina Ouedjedi, Arnaud Rougirel, Khaled BenmeriemThis paper gathers the tools for solving RiemannLiouville time fractional nonlinear PDE’s by using a Galerkin method. This method has the advantage of not being more complicated than the one used to solve the same PDE with first order time derivative. As a model problem, existence and uniqueness is proved for semilinear heat equations with polynomial growth at infinity.

Müntz sturmliouville problems: Theory and numerical experiments Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Hassan KhosravianArab, Mohammad Reza EslahchiThis paper presents two new classes of Müntz functions which are called JacobiMüntz functions of the first and second types. These newly generated functions satisfy in two selfadjoint fractional SturmLiouville problems and thus they have some spectral properties such as: orthogonality, completeness, threeterm recurrence relations and so on. With respect to these functions two new orthogonal projections

Simultaneous inversion for the fractional exponents in the spacetime fractional diffusion equation ∂tβ u = −(− Δ)α/2u − (− Δ)γ/2u Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Ngartelbaye Guerngar, Erkan Nane, Ramazan Tinaztepe, Suleyman Ulusoy, Hans Werner Van WykIn this article, we consider the spacetime fractional (nonlocal) equation characterizing the socalled “doublescale” anomalous diffusion ∂ tβ u(t,x)=− (− Δ )α /2u(t,x)− (− Δ )γ /2u(t,x),t> >0,− 1< x< 1,$$\begin{array}{} \displaystyle \partial_t^\beta u(t, x) = (\Delta)^{\alpha/2}u(t,x)  (\Delta)^{\gamma/2}u(t,x), \, \, t \gt 0, \, 1 \lt x \lt 1, \end{array}$$ where ∂ tβ $\begin{array}{} \displaystyle

Nonlinear convolution integrodifferential equation with variable coefficient Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Sultan N. AskhabovFor an integrodifferential equation of the convolution type defined on the halfline [0, ∞) with a power nonlinearity and variable coefficient, we use the weight metrics method to prove a global theorem on the existence and uniqueness of a solution in the cone of nonnegative functions in the space C [0, ∞). It is shown that the solution can be found by a successive approximation method of the Picard

An efficient localized collocation solver for anomalous diffusion on surfaces Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Zhuochao Tang, Zhuojia Fu, HongGuang Sun, Xiaoting LiuThis paper introduces an efficient collocation solver, the generalized finite difference method (GFDM) combined with the recentdeveloped scaledependent time stepping method (SDTSM), to predict the anomalous diffusion behavior on surfaces governed by surface timefractional diffusion equations. In the proposed solver, the GFDM is used in spatial discretization and SDTSM is used in temporal discretization

Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210601
Tadeusz Kaczorek, Łukasz SajewskiThe global stability of continuoustime fractional orders nonlinear feedback systems with positive linear parts and interval state matrices is investigated. New sufficient conditions for the global stability of this class of positive feedback nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple example.

Frontmatter Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Article Frontmatter was published on April 1, 2021 in the journal Fractional Calculus and Applied Analysis (volume 24, issue 2).

Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021) Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Virginia KiryakovaArticle Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021) was published on April 1, 2021 in the journal Fractional Calculus and Applied Analysis (volume 24, issue 2).

Operational calculus for the general fractional derivative and its applications Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Yuri LuchkoIn this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero. Both particular cases and compositions of these operators are discussed. Then we proceed with a construction of an operational calculus of the Mikusiński type for the general fractional derivatives with the Sonine

Riesz potentials and orthogonal radon transforms on affine Grassmannians Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Boris Rubin, Yingzhan WangWe establish intertwining relations between Riesz potentials associated with fractional powers of minusLaplacian and orthogonal Radon transforms 𝓡 j , k of the GonzalezStrichartz type. The latter take functions on the Grassmannian of j dimensional affine planes in ℝ n to functions on a similar manifold of k dimensional planes by integration over the set of all j planes that meet a given k plane

Characterizations of variable martingale Hardy spaces via maximal functions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Ferenc WeiszWe introduce a new type of dyadic maximal operators and prove that under the logHölder continuity condition of the variable exponent p (⋅), it is bounded on L p (⋅) if 1 < p − ≤ p + ≤ ∞. Moreover, the space generated by the L p (⋅) norm (resp. the L p (⋅), q norm) of the maximal operator is equivalent to the Hardy space H p (⋅) (resp. to the HardyLorentz space H p (⋅), q ). As special cases, our

Contributions on artificial potential field method for effective obstacle avoidance Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
JeanFrançois Duhé, Stéphane Victor, Pierre MelchiorObstacle avoidance is one of the main interests regarding path planning. In many situations (mostly those regarding applications in urban environments), the obstacles to be avoided are dynamical and unpredictable. This lack of certainty regarding the environment introduces the need to use local path planning techniques rather than global ones. A wellknown method uses artificial potential fields introduced

Selfsimilar cauchy problems and generalized MittagLeffler functions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Pierre Patie, Anna SrapionyanBy observing that the fractional Caputo derivative of order α ∈ (0, 1) can be expressed in terms of a multiplicative convolution operator, we introduce and study a class of such operators which also have the same selfsimilarity property as the Caputo derivative. We proceed by identifying a subclass which is in bijection with the set of Bernstein functions and we provide several representations of

Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Mohammed D. Kassim, Nassereddine TatarThe asymptotic behaviour of solutions in an appropriate space is discussed for a fractional problem involving Hadamard leftsided fractional derivatives of different orders. Reasonable sufficient conditions are determined ensuring that solutions of fractional differential equations with nonlinear right hand sides approach a logarithmic function as time goes to infinity. This generalizes and extends

A boundary value problem for a partial differential equation with fractional derivative Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Menglibay RuzievIn this paper, we investigate a nonlocal boundary value problem for an equation of special type. For y > 0 it is a fractional diffusion equation, which contains the RiemannLiouville fractional derivative. For y < 0 it is a generalized equation of moisture transfer. A unique solvability of the considered problem is proved.

Operational calculus for the Riemann–Liouville fractional derivative with respect to a function and its applications Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Hafiz Muhammad Fahad, Arran FernandezMikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has been applied to several types of fractionalcalculus operators by Y. Luchko and collaborators, such as for example [26], etc. In this paper, we consider the operators of Riemann–Liouville fractional differentiation of a function with respect to another function

Duality theory of fractional resolvents and applications to backward fractional control systems Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Shouguo Zhu, Gang LiWe study the duality theory for fractional resolvents, extending and improving some corresponding theorems on semigroups. As applications, we develop the variational technique to analyze the finiteapproximate controllability of a backward fractional control system with a rightsided RiemannLiouville fractional derivative. Moreover, validity of our theoretical findings is given by a fractional diffusion

Kinetic solutions for nonlocal stochastic conservation laws Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Guangying Lv, Hongjun Gao, Jinlong WeiThis work is devoted to examining the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal supercritical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation.

A fractional analysis in higher dimensions for the SturmLiouville problem Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Milton Ferreira, M. Manuela Rodrigues, Nelson VieiraIn this work, we consider the n dimensional fractional SturmLiouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right RiemannLiouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the

Averaging theory for fractional differential equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210401
Guanlin Li, Brad LehmanThe theory of averaging is a classical component of applied mathematics and has been applied to solve some engineering problems, such as in the filed of control engineering. In this paper, we develop a theory of averaging on both finite and infinite time intervals for fractional nonautonomous differential equations. The closeness of the solutions of fractional noautonomous differential equations

Frontmatter Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Article Frontmatter was published on February 1, 2021 in the journal Fractional Calculus and Applied Analysis (volume 24, issue 1).

FCAA related news, events and books (FCAA–volume 24–1–2021) Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Virginia KiryakovaArticle FCAA related news, events and books (FCAA–volume 24–1–2021) was published on February 1, 2021 in the journal Fractional Calculus and Applied Analysis (volume 24, issue 1).

Renormalization group and fractional calculus methods in a complex world: A review Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Lihong Guo, YangQuan Chen, Shaoyun Shi, Bruce J. WestThe concept of the renormalization group (RG) emerged from the renormalization of quantum field variables, which is typically used to deal with the issue of divergences to infinity in quantum field theory. Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity

On the asymptotics of wright functions of the second kind Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Richard B. Paris, Armando Consiglio, Francesco MainardiThe asymptotic expansions of the Wright functions of the second kind, introduced by Mainardi [see Appendix F of his book Fractional Calculus and Waves in Linear Viscoelasticity (2010)], Fσ(x)=∑n=0∞(−x)nn!Γ(−nσ) , Mσ(x)=∑n=0∞(−x)nn!Γ(−nσ+1−σ) (0<σ<1)$$F_\sigma(x)=\sum\limits_{n=0}^\infty \frac{(x)^n}{n! {\mathrm{\Gamma}}(n\sigma)}~,\quad M_\sigma(x)=\sum\limits_{n=0}^\infty \frac{(x)^n}{n! {\mat

On fractional heat equation Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Anatoly N. Kochubei, Yuri Kondratiev, José Luís da SilvaIn this paper, the longtime behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the CaputoDjrbashian fractional derivative and more general cases corresponding to differentialconvolution operators, in particular, distributed order

Completely monotone multinomial mittagleffler type functions and diffusion equations with multiple timederivatives Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Emilia BazhlekovaThe multinomial MittagLeffler function plays a crucial role in the study of multiterm timefractional evolution equations. In this work we establish basic properties of the Prabhakar type generalization of this function with the main emphasis on complete monotonicity. As particular examples, the relaxation functions for equations with multiple timederivatives in the socalled “natural” and “modified”

A fractional generalization of the dirichlet distribution and related distributions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Elvira Di Nardo, Federico Polito, Enrico ScalasThis paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, W n ] are independent and identically distributed random variables following the generalized MittagLeffler distribution. The expected value and variance of the onedimensional marginal are derived as well as the

Should i stay or should i go? zerosize jumps in random walks for lévy flights Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Gianni Pagnini, Silvia VitaliWe study Markovian continuostime random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bimodal powerlaw distribution that is equal to zero in zero. The significance of this result is twofold: i ) with regard to the probabilistic derivation of the fractional diffusion equation and also ii ) with regard to the

Wellposedness for weak and strong solutions of nonhomogeneous initial boundary value problems for fractional diffusion equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Yavar Kian, Masahiro YamamotoWe study the wellposedness for initial boundary value problems associated with time fractional diffusion equations with nonhomogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak solutions, we introduce a definition of solutions which allows to prove the existence of solution to the initial boundary value problems with nonzero initial and boundary

Error analysis of nonlinear time fractional mobile/immobile advectiondiffusion equation with weakly singular solutions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Hui Zhang, Xiaoyun Jiang, Fawang LiuIn this paper, a weighted and shifted GrünwaldLetnikov difference (WSGD) Legendre spectral method is proposed to solve the twodimensional nonlinear time fractional mobile/immobile advectiondispersion equation. We introduce the correction method to deal with the singularity in time, and the stability and convergence analysis are proven. In the numerical implementation, a fast method is applied based

Exact stability and instability regions for twodimensional linear autonomous multiorder systems of fractionalorder differential equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Oana Brandibur, Eva KaslikNecessary and sufficient conditions are explored for the asymptotic stability and instability of linear twodimensional autonomous systems of fractionalorder differential equations with Caputo derivatives. Fractionalorderdependent and fractionalorderindependent stability and instability properties are fully characterised, in terms of the main diagonal elements of the systems’ matrix, as well as

On a method of solution of systems of fractional pseudodifferential equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Sabir Umarov, Ravshan Ashurov, YangQuan ChenThis paper is devoted to the general theory of linear systems of fractional order pseudodifferential equations. Single fractional order differential and pseudodifferential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudodifferential

Monte carlo estimation of the solution of fractional partial differential equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Vassili Kolokoltsov, Feng Lin, Aleksandar MijatovićThe paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of errors between the exact solution and the Monte Carlo approximation, the estimate of the fluctuation via the appropriate central limit theorem (CLT) and the construction

Stability analysis for discrete time abstract fractional differential equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Jia Wei He, Yong ZhouIn this paper, we consider a discretetime fractional model of abstract form involving the RiemannLiouvillelike difference operator. On account of the C 0 semigroups generated by a closed linear operator A and based on a distinguished class of sequences of operators, we show the existence of stable solutions for the nonlinear Cauchy problem by means of fixed point technique and the compact method

Existence of local solutions for fractional difference equations with left focal boundary conditions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20210201
Johnny Henderson, Jeffrey T. NeugebauerFor 1 < ν ≤ 2 a real number and T ≥ 3 a natural number, conditions are given for the existence of solutions of the ν th order AtıcıEloe fractional difference equation, Δ ν y ( t ) + f ( t + ν − 1, y ( t + ν − 1)) = 0, t ∈ {0, 1, …, T }, and satisfying the left focal boundary conditions Δ y ( ν − 2) = y ( ν + T ) = 0.

Frontmatter Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201231
Journal Name: Fractional Calculus and Applied Analysis Volume: 23 Issue: 6 Pages: iv

Fractional derivatives and cauchy problem for differential equations of fractional order Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
M.M. Dzherbashian, A.B. NersesianAbstract Editorial Note: This is a paper by M.M. Djrbashian and A.B. Nersesian of 1968, that was published in Russian. There is a constant interest to Djrbashian’s contributions to the topic of fractional calculus and theory of MittagLeffler function. Unfortunately, his works were published in Russian and thus, are not easy accessible and not enough popular. Therefore, we invited hS. Rogosin and M

Mkhitar Djrbashian and his contribution to Fractional Calculus Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Sergei Rogosin, Maryna DubatovskayaAbstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (19181994) is a wellknown expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties

Implementation of fractional optimal control problems in realworld applications Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Neelam SinghaAbstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractionalorder model describes the interaction of effectorimmune cells and tumor cells, including combined chemoimmunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractionalorder

Fractional nonlinear stochastic heat equation with variable thermal conductivity Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Miloš Japundžić, Danijela RajterĆirićAbstract We consider a nonlinear stochastic heat equation with Riesz spacefractional derivative and variable thermal conductivity, on infinite domain. First we approximate the original problem by regularizing the Riesz spacefractional derivative. Then we prove that the approximate problem has almost surely a unique solution within a Colombeau generalized stochastic process space. In our solving procedure

Bounded solutions of second order of accuracy difference schemes for semilinear fractional schrödinger equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Allaberen Ashyralyev, Betul HicdurmazAbstract The present paper deals with initial value problem (IVP) for semilinear fractional Schrödinger integrodifferential equation idudt+Au=∫0tfs,Dsαu(s)ds,0

Nakhushev extremum principle for a class of integrodifferential operators Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Arsen PskhuAbstract We investigate extreme properties of a class of integrodifferential operators. We prove an assertion that extends the Nakhushev extremum principle, known for fractional RiemannLiouville derivatives, to integrodifferential operators with kernels of a general form. We establish the weighted extremum principle for convolution operators and the RiemannLiouville fractional derivative. In addition

Uniqueness for an inverse source problem of determining a spacedependent source in a nonautonomous timefractional diffusion equation Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Marian SlodičkaAbstract We study uniqueness of a solution for an inverse source problem arising in linear timefractional diffusion equations with timedependent coefficients. We consider source term in a separated form h(t)f (x). The unknown source f (x) is recovered from the final time measurement u (x, T). A new uniqueness result is formulated in Theorem 3.1 under the assumption that h ∈ C ([0, T]) and 0 ≢ h ≥

Determination of timedependent sources and parameters of nonlocal diffusion and wave equations from final data Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Jaan JannoAbstract Two inverse problems with final overdetermination for diffusion and wave equations containing the Caputo fractional time derivative and a fractional Laplacian of distributed order are considered. They are: 1) the problem to reconstruct a timedependent source term; 2) the problem to recover simultaneously the source term, the order of the time derivative and the fractional Laplacian. Uniqueness

Multidimensional van der CorputType estimates involving MittagLeffler functions Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Michael Ruzhansky, Berikbol T. TorebekAbstract The paper is devoted to study multidimensional van der Corputtype estimates for the intergrals involving MittagLeffler functions. The generalisation is that we replace the exponential function with the MittagLefflertype function, to study multidimensional oscillatory integrals appearing in the analysis of timefractional evolution equations. More specifically, we study two types of integrals

Determination of the order of fractional derivative for subdiffusion equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Ravshan Ashurov, Sabir UmarovAbstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring

A survey on numerical methods for spectral SpaceFractional diffusion problems Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Stanislav Harizanov, Raytcho Lazarov, Svetozar MargenovAbstract The survey is devoted to numerical solution of the equation Aαu=f $ {\mathcal A}^\alpha u=f $ , 0 < α<1, where A $ {\mathcal A} $ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain Ω in ℝd. The fractional power Aα $ {\mathcal A}^\alpha $ is a nonlocal operator and is defined though the spectrum of A $ {\mathcal A}

Wave propagation dynamics in a fractional Zener model with stochastic excitation Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Teodor Atanacković, Stevan Pilipović, Dora SelešiAbstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the KarhunenLoéve expansion theorem are

FCAA special 2020 conferences' issue (FCAA–Volume 23–6–2020) Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201216
Virginia KiryakovaIn 2020 some international conferences on Fractional Calculus (FC) and related topics have been held in a hybrid way mainly online via popular electronic platforms and by physical presence with reduced number of local participants. Despite of the pandemic situation, the FC community showed as usual great activities. In this special issue, we collected some of the plenary presentations and invited selected

The asymptotic behavior of solutions of discrete nonlinear fractional equations Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201113
Mustafa Bayram, Aydin Secer, Hakan AdiguzelIn this study, we consider a class of nonlinear fractional difference equations following form:

Frontmatter Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201113
Journal Name: Fractional Calculus and Applied Analysis Volume: 23 Issue: 5 Pages: iv

Cauchy problem for general time fractional diffusion equation Fract. Calc. Appl. Anal. (IF 3.126) Pub Date : 20201001
ChungSik SinAbstract In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputotype differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis technique. Then, based on the representation