The Numerical Treatment of Some Fractional Partial Differential Equations with Error Estimation

Abstract Some important engineering and physics problems are modeled by linear/nonlinear fractional partial differential equations. The main objective of the study is to solve such types of problems by extending the Legendre collocation method with a fractional operational matrix. After the derivation of this matrix, the developed approach converts the problem into an algebraic system of equations based on orthogonal Legendre polynomials. Numerical examples are provided for demonstration. The error estimation demonstrates the efficiency and dependability of the suggested strategy.