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This paper provides a new optimization technique for solving fractional hyperbolic and reaction-diffusion equations with nonlocal boundary conditions. Base on Euler scaling functions (ESFs) and operational matrices of integration and derivative, we develop the optimization method to get the approximate solution with high precision. In the process of the numerical algorithm, by applying the operational matrices, we transform the problems into a system of algebraic equations. It should be noted that we investigate and analyze the method error. Eventually, to confirm the applicability of the explained approach, we examine several examples and demonstrate the results in tables and graphical curves.

numerical functional analysis and optimization

Composition of Euler Scaling Functions with the Optimization Method for Fractional Hyperbolic and Reaction-Diffusion Equations with Nonlocal Boundary Conditions