Theoretical and numerical studies of fractional Volterra-Fredholm integro-differential equations in Banach space
This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer’s fixedpoint theorem, the Banach contraction theorem and the Arzelà-Ascoli theorem, we establish some conditions that...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universiti Putra Malaysia
2024
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/114421/ http://psasir.upm.edu.my/id/eprint/114421/1/114421.pdf |
| Summary: | This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional
Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer’s fixedpoint
theorem, the Banach contraction theorem and the Arzelà-Ascoli theorem, we establish
some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the
stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman’s inequality.
Additionally, the Laplace Adomian decomposition method (LADM) is employed to
obtain the approximate solutions for both linear and non-linear FVFIDEs. The method’s efficiency
is demonstrated through some numerical examples. |
|---|