Analytical solutions of fuzzy fractional boundary value problem of order 2α by using RKHS algorithm

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.