Abstract
Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann–Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed method.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference28 articles.
1. Analytical solution of time-fractional Schrödinger equations via Shehu Adomian Decomposition Method;Kapoor;AIMS Math.,2022
2. Ozkan, E.M. (2022). New exact solutions of some important nonlinear fractional partial differential Equations with beta derivative. Fractal Fract., 6.
3. A local projection stabilization virtual element method for the time-fractional Burgers equation with high Reynolds numbers;Zhang;Appl. Math. Comput.,2023
4. Iqbal, J., Shabbir, K., and Guran, L. (2022). Stability analysis and computational interpretation of an effective semi analytical scheme for fractional order non-linear partial differential equations. Fractal Fract., 6.
5. Alshehry, A.S., Imran, M., Khan, A., Shah, R., and Weera, W. (2022). Fractional view analysis of Kuramoto-Sivashinsky equations with non-singular kernel operators. Symmetry, 14.
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