2024 Volume 14 Issue 6
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D. Sh. Mohamed, M. A. Abdou, A. M. S. Mahdy. DYNAMICAL INVESTIGATION AND NUMERICAL MODELING OF A FRACTIONAL MIXED NONLINEAR PARTIAL INTEGRO-DIFFERENTIAL PROBLEM IN TIME AND SPACE[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3458-3479. doi: 10.11948/20240050
Citation: D. Sh. Mohamed, M. A. Abdou, A. M. S. Mahdy. DYNAMICAL INVESTIGATION AND NUMERICAL MODELING OF A FRACTIONAL MIXED NONLINEAR PARTIAL INTEGRO-DIFFERENTIAL PROBLEM IN TIME AND SPACE[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3458-3479. doi: 10.11948/20240050
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DYNAMICAL INVESTIGATION AND NUMERICAL MODELING OF A FRACTIONAL MIXED NONLINEAR PARTIAL INTEGRO-DIFFERENTIAL PROBLEM IN TIME AND SPACE

  • 1.

    Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

  • 2.

    Department of Mathematics, Faculty of Education, Alexandria University, P.O. Box 21526, Alexandria, Egypt

  • 3.

    Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    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.

    MSC: 65R20, 45M10, 35R09
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