FRACTIONAL VARIATIONAL PROBLEM INVOLVING INDEFINITE INTEGRALS AND NONSINGULAR KERNELS

Abstract

This paper deals with a class of fractional variational problems involving Atangana–Baleanu (AB) derivative. The problem under consideration is a graceful combination of AB derivative with indefinite integral. A proposed numerical technique based on the shifted Vieta–Lucas polynomials is utilized for obtaining the solutions to the given problem. Our numerical process is principally based on the operational matrix (OM) of fractional integral in the AB sense in order to approximate solutions of the problem under study. By utilizing the OM along with the Lagrange multiplier method, the given problems are converted into a problem easier to solve. The resultant problem can then be solved using standard methods. Convergence of the presented method is investigated. In order to ensure and display the efficiency and accuracy of the proposed technique, some examples are given.