Abstract
This paper investigates a computational method to find an approximation to the solution of fractional differential equations subject to local and nonlocal m-point boundary conditions. The method that we will employ is a variant of the spectral method which is based on the normalized Bernstein polynomials and its operational matrices. Operational matrices that we will developed in this paper have the ability to convert fractional differential equations together with its nonlocal boundary conditions to a system of easily solvable algebraic equations. Some test problems are presented to illustrate the efficiency, accuracy, and applicability of the proposed method.
Highlights
The studies of fractional differential equations (FDEs) gained the attention of many scientists around the globe
In this article we present an approximation procedure to find an approximate solution of the FDEs subject to local and nonlocal m-point boundary value problems (BVPs)
We develop four operational matrices, two of them being operational matrices of integration and differentiation, the formulation technique for these two operational matrices is the same as that used for traditional orthogonal polynomials
Summary
The studies of fractional differential equations (FDEs) gained the attention of many scientists around the globe. The authors in [ – ] extended the spectral method to find a smooth approximation to various classes of FDEs and FPDEs. Some recent results in which orthogonal polynomials are applied to solve various scientific problems can be found in [ – ]. We use a triple product for Bernstein polynomials to construct a new operational matrix which is of basic importance in solving FDEs with variable coefficients.
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