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This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Masahiro Yamamoto

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative…

Classical Analysis and ODEs · Mathematics 2018-09-05 Xiao-Jun Yang , Feng Gao , J. A. Tenreiro Machado , Dumitru Baleanu

In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients.…

Numerical Analysis · Mathematics 2016-09-27 Xiaogang Zhu , Yufeng Nie

In this paper the Sumudu transforms of Hilfer-Prabhakar fractional derivative and regularized version of Hilfer-Prabhakar fractional derivative are obtained. These results are used to obtain relation between them involving Mittag- Leffler…

Classical Analysis and ODEs · Mathematics 2016-09-22 S. K. Panchal , Amol D. Khandagale , Pravinkumar V. Dole

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…

Analysis of PDEs · Mathematics 2018-08-13 Zhiyuan Li , Kenichi Fujishiro , Gongsheng Li

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…

Numerical Analysis · Mathematics 2020-01-27 Wesley Davis , Richard Noren , Ke Shi

In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…

Numerical Analysis · Mathematics 2025-08-15 Hameed Ullah Jan , Marjan Uddin , Irshad Ali Shah , Salam Ullah Khan

In the present research article, we investigate solutions for fractional kinetic equations, involving $\mathtt{k}$-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based. the…

Classical Analysis and ODEs · Mathematics 2016-12-20 Kottakkaran Sooppy Nisar , Saiful Rahman Mondal , F. B. M. Belgacem

This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…

Analysis of PDEs · Mathematics 2023-05-23 Anani Kwassi

In this study, we combine two novel methods, the conformable double Laplace-Sumudu transform (CDLST) and the modified decomposition technique. We use the new approach called conformable double Laplace-Sumudu modified decomposition (CDLSMD)…

General Mathematics · Mathematics 2023-06-07 S. A. Ahmed , R. Saadeh , A. Qazza , T. M. Elzaki

We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…

Analysis of PDEs · Mathematics 2013-04-04 Roberto Garra , Federico Polito

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…

Numerical Analysis · Mathematics 2015-12-16 Ricardo Almeida , Nuno R. O. Bastos

Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…

Analysis of PDEs · Mathematics 2017-12-21 Uttam Ghosh , Md Ramjan Ali , Santanu Raut , Susmita Sarkar , Shantanu Das

In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…

Numerical Analysis · Mathematics 2022-06-08 Kamlesh Kumar , Rajesh K. Pandey

Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…

Numerical Analysis · Mathematics 2011-03-23 Tamás Ladics

We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…

Classical Analysis and ODEs · Mathematics 2009-09-25 M. Lawrence Glasser , Victor Kowalenko

We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…

Analysis of PDEs · Mathematics 2018-02-08 Adam Kubica , Katarzyna Ryszewska

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…

Data Analysis, Statistics and Probability · Physics 2018-04-30 R. A. Treumann , W. Baumjohann

Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…

Mesoscale and Nanoscale Physics · Physics 2024-08-06 Kyle Rockwell , Ezio Iacocca

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti