2024 : 3 : 29
Hossein Jafari

Hossein Jafari

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 2466

Research

Title
A new numerical scheme for solving pantograph type nonlinear fractional integro-differential equations
Type
JournalPaper
Keywords
Non-local and non-singular kernel, Volterra nonlinear fractional integrodifferential equations, Atangana–Baleanu operator, The shifted Legendre polynomials, Approximation solution
Year
2021
Journal JOURNAL OF KING SAUD UNIVERSITY SCIENCE
DOI
Researchers Hossein Jafari ، Nguyen Huy Tuan ، Roghayeh Moallem Ganji

Abstract

In this work, a general class of pantograph type nonlinear fractional integro-differential equations (PTFIDEs) with non-singular and non-local kernel is considered. A numerical scheme based on the orthogonal basis functions including the shifted Legendre polynomials (SLPs) is proposed. First, we expand the unknown function and its derivatives in terms of the SLPs with unknown coefficients. Then, we present several theorems based on the SLPs for the help to achieve the approximate solution of the problem under study. Finally, by utilizing these theorems together with the collocation points, the main problem is transformed to a system of linear or nonlinear algebraic equations, which can be simply solved. An investigation for error estimate is discussed. The accuracy and efficiency of the proposed scheme are reported by four illustrative examples