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Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
Numerical solution of variable-order fractional integro-partial differential equations via Sinc collocation method based on single and double exponential transformations
Type
JournalPaper
Keywords
Variable-order fractional calculus, Integro-partial differential equations, Diffusion equation, Sinc function, Numerical analysis, Spline approximation, Convergence and error
Year
2020
Journal Communications in Nonlinear Science and Numerical Simulation
DOI
Researchers Afshin Babaei ، Behrouz Parsa Moghaddam ، ُSeddighe Banihashemi ، Jose Antonio Tenreiro Machado

Abstract

This paper addresses the numerical solution of the multi-dimensional variable-order fractional integro-partial differential equations. The upwind scheme and a piecewise linear interpolation, are proposed to approximate the Coimbra variable-order fractional derivatives and integral term with kernel, respectively. Two new approaches via the Sinc collocation method based on single and double exponential transformations are adopted for the temporal and spatial discretizations, respectively. The convergence behaviour of the methods is analysed and the error bounds are provided. In addition, four test problems illustrate the validity and effectiveness of the proposed algorithms.