Numerical Solution of Conformable Fractional Periodic Boundary Value Problems by Shifted Jacobi Method

This paper presents the so-called shifted Jacobi method, an efficient numerical technique to solve second-order periodic boundary value problems with finitely many singularities involving nonlinear systems of two points. The method relies on the Jacobi polynomials used as natural basis functions in the conformable sense of fractional derivative. A study is carried out to compare the outcomes of the shifted Jacobi approach with those of other methods that are currently in use. In the same vein, a theoretical result for establishing a bound of the error generated from the proposed approximate solution is proved accordingly. The efficiency and effectiveness of the shifted Jacobi technique with conformable fractional derivative are discussed numerically.