Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

Abstract

This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractionalorder partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

“…In [33], a system of fractional differential equations was solved by the homotopy analysis method. Some recent work in this field was done by Hassani et al [34]. The authors proposed a method for solving a system of nonlinear fractional-order partial differential equations with initial conditions.…”