On the Convergence of a Spline Collocation Method for Nonlinear Fractional Boundary Value Problems with the Riesz-Caputo Operator
Provides theoretical and numerical foundations for solving a class of fractional boundary value problems, which is incremental for researchers in fractional calculus.
The paper proves existence and uniqueness for nonlinear fractional boundary value problems with the Riesz-Caputo operator and introduces a B-spline collocation method with convergence analysis, supported by numerical experiments.
Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo operator, which is particularly suited for modeling physical phenomena exhibiting symmetric diffusive effects. We provide an integral representation of the solution to prove existence and uniqueness of the fractional differential problem. We introduce a B-spline collocation method to approximate the solution of the problem and provide a convergence analysis, with both theoretical insights and numerical experiments.