Quasi-Interpolant Operators and the Solution of Fractional Differential Problems

TL;DR

This paper introduces a collocation method using spline quasi-interpolants to efficiently and accurately solve boundary value problems involving fractional derivatives, addressing the challenge of limited analytical solutions.

Contribution

It presents a novel collocation approach with spline quasi-interpolants for fractional differential equations, simplifying the numerical solution process.

Findings

Method is efficient based on numerical tests.

Approximations are accurate for fractional boundary value problems.

Spline quasi-interpolants effectively handle fractional derivatives.

Abstract

Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their solution. In this paper we are interested in solving boundary value problems having space derivative of fractional order. To this end, we present a collocation method in which the solution of the fractional problem is approximated by a spline quasi-interpolant operator. This allows us to construct the numerical solution in an easy way. We show through some numerical tests that the proposed method is efficient and accurate.