2024 : 6 : 17
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
An algorithmic exploration of variable order fractional partial integro-differential equations via hexic shifted Chebyshev polynomials
Type
JournalPaper
Keywords
Partial integro differential equation, Variable-order fractional calculus, Collocation method, Convergence analysis
Year
2024
Journal Computational and Applied Mathematics
DOI
Researchers Afshin Babaei ، ُSeddighe Banihashemi ، Behrouz Parsa Moghaddam ، Arman Dabiri

Abstract

The focus of this investigation centers on the formulation of a novel spectral method deployed to numerically solve partial integro-differential equations that possess memory features. The approach leverages the hexic shifted Chebyshev polynomials, and addresses the nonlinearity of the computational output using iterative methods. A comprehensive explanation of the methodology is presented, and a thorough convergence analysis is conducted. This technique has the capacity to be effortlessly modified and used to solve a plethora of linear and nonlinear issues, while minimizing computational time. Ultimately, the effectiveness of this novel strategy is demonstrated through the successful resolution of two exemplary problems. The findings of this study suggest that this spectral approach holds significant promise for solving partial integro-differential equations.