| Volume 14, Number 6, 2024, Pages - DOI：10.11948/JAAC-2024-0050 |
| Dynamical investigation and numerical modeling of a fractional mixed nonlinear partial integro-differential problem in time and space |
| Amr Mahdy |
| Keywords:Fractional integral equations, Mixed integral equations, Separation of variables, Chebyshev polynomials of the sixth- kind, Caputo fractional derivative. |
| Abstract: |
| In the current study, a novel and effective method for solving the
nonlinear fractional mixed partial integro-differential equation
(NfrPIo-DE) based on a continuous kernel is presented and
discussed. The NfrPIo-DE is transformed into the nonlinear
Fredholm integral equation (NFIE) through the utilization of the
separation of variables. The NFIE reduction was then transformed
into a system of nonlinear algebraic equations (SNAE) with the
application of Chebyshev polynomials of the sixth type (CP6K). By
utilizing the Banach fixed point theorem, we can describe the
existence of the solution of NfrPIo-DE as well as its uniqueness.
Furthermore, the convergence and the stability of the reduced
error have been described. Finally, a numerical example is presented
to illustrate the theoretical results. The Maple 18 software is
responsible for getting all of the computational outcomes. |
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