An Investigation on Existence, Uniqueness, and Approximate Solutions for Two-Dimensional Nonlinear Fractional Integro-Differential Equations

Tahereh Eftekhari () and Jalil Rashidinia
Additional contact information
Tahereh Eftekhari: School of Mathematics, Iran University of Science & Technology (IUST), Narmak, Tehran 16846 13114, Iran
Jalil Rashidinia: School of Mathematics, Iran University of Science & Technology (IUST), Narmak, Tehran 16846 13114, Iran

Mathematics, 2023, vol. 11, issue 4, 1-29

Abstract: In this research, we provide sufficient conditions to prove the existence of local and global solutions for the general two-dimensional nonlinear fractional integro-differential equations. Furthermore, we prove that these solutions are unique. In addition, we use operational matrices of two-variable shifted Jacobi polynomials via the collocation method to reduce the equations into a system of equations. Error bounds of the presented method are obtained. Five test problems are solved. The obtained numerical results show the accuracy, efficiency, and applicability of the proposed approach.

Keywords: the mixed Riemann–Liouville integral; fixed-point theorems; shifted Jacobi polynomials; operational matrices; collocation method; error bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/4/824/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/4/824/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:4:p:824-:d:1059433

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().