Author:
Ahmed A. I.,Al-Sharif M. S.
Abstract
AbstractIn this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.
Funder
Open access funding provided by The Science, Technology amp; Innovation Funding Authority(STDF) in cooperation with The Egyptian Knowledge Bank
Al-Azhar University
Publisher
Springer Science and Business Media LLC
Reference50 articles.
1. Abdo, M., Panchal, S.: Existence and uniqueness results for fractional differential equations with infinite delay. Dyn. Contin. Discrete Impuls. Syst., Ser. A Math. Anal. 26, 205–216 (2019)
2. Ahmad, M.Z., Alsarayreh, D., Alsarayreh, A., Qaralleh, I.: Differential transformation method (DTM) for solving SIS and SI epidemic models. Sains Malays. 46, 2007–2017 (2017)
3. Ahmed, A.I., Al-Ahmary, T.A.: Fractional-order Chelyshkov collocation method for solving systems of fractional differential equations. Math. Probl. Eng. 2022, 4862650 (2022)
4. Ahmed, A.I., Al-Sharif, M.S., Salim, M.S., Al-Ahmary, T.A.: Numerical solution of fractional variational and optimal control problems via fractional-order Chelyshkov functions. AIMS Math. 7(9), 17418–17443 (2022)
5. Al-Sharif, M.S., Ahmed, A.I., Salim, M.S.: An integral operational matrix of fractional-order Chelyshkov functions and its applications. Symmetry 12(11), 1755 (2020)