Analytical Solutions of Fuzzy Fractional Boundary Value Problem of Order 2α by Using RKHS Algorithm

Authors

Mohammad Abdel Aal, Department of Basic Sciences, Faculty of Art and Science, Middle East University, Amman, JordanFollow
Nisrein Abu-Darwish, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanFollow
Omar Abu Arqub, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow
Mohammed Al-Smadi, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow
Shaher Momani, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan\\ Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi ArabiaFollow

Author Country (or Countries)

Jordan

Abstract

In this article, an effective numerical solution for fractional fuzzy differential equations of order 2α subject to appropriate fuzzy boundary conditions has been provided by using the Reproducing Kernel (RK) algorithm in Caputo sense. The reproducing kernel functions are built, in which the constraint conditions are satisfied, to yield a fast and accurate RK algorithm for handling these BVPs. The solution methodology is based on constructing the fractional series solution based on the reproducing-kernel theory in the form of a rapidly convergent series with a minimum size of calculations using symbolic computation software. The analytical solution is formulated in the form of a finite series, while, the n-term numerical solution is obtained and proved to converge uniformly to the analytical solution in the space of interest. Simulations, as well as the computational algorithm, are provided to guarantee the RK procedure, to show potentiality, generality, and superiority of RK algorithm and to illustrate the theoretical statements of the present algorithm.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/130402

Recommended Citation

Abdel Aal, Mohammad; Abu-Darwish, Nisrein; Abu Arqub, Omar; Al-Smadi, Mohammed; and Momani, Shaher (2019) "Analytical Solutions of Fuzzy Fractional Boundary Value Problem of Order 2α by Using RKHS Algorithm," Applied Mathematics & Information Sciences: Vol. 13: Iss. 4, Article 2.
DOI: http://dx.doi.org/10.18576/amis/130402
Available at: https://digitalcommons.aaru.edu.jo/amis/vol13/iss4/2