Existence and Uniqueness of the approximation Solutions To the Boundary Value Problem for Fractional Sturm-Liouville Differential Equations with the Caputo Derivative (Journal of Humanitarian and Applied Sciences, 2023)
Abstract:In this paper, the researcher investigated the Fractional Sturm–Liouville boundary value problem with the Caputo derivative and studied the existence and uniqueness of its solution in Banach space, in addition to the continuation of its solution. As the result, researcher proved some theorems on the existence of solutions for FSLP and then extend a Fixed-Point theorem for ODEs to this of the Fractional Sturm–Liouville problem with boundary conditions. Also, the given problem by obtained via the constructing approximate solution by Picard and Krasnoselskij-Mann iterations.
Keywords: Fractional Sturm–Liouville Problem; Caputo fractional derivatives; iterative methods; contraction and non-expansive mapping; Fixed-Point theorem