Approximate Solution of Fractional Integro-Differential Equations by Least Squares Method

In this paper, least squares approximation method is developed for solving a class of linear fractional integro-differential equations comprising Volterra and Fredhlom cases. This method is based on a polynomial of degree n to compute an approximate solution of these equations. The convergence analysis of the proposed method is proved. In addition, to show the accuracy and the efficiency of the proposed method, some examples are presented

A new operational matrix for solving two-dimensional nonlinear integral equations of fractional order

In this paper, first, we derive the operational matrix of two-dimensional orthogonal triangular functions (2D-TFs) for two-dimensional fractional integrals. Then, we apply this operational matrix and properties of Two-dimensional orthogonal triangular functions to reduce two-dimensional fractional integral equations to a system of algebraic equations. Finally, in order to show the validity and efficiency, we present some numerical examples

Approximate Solution of Fractional Integro-Differential Equations by Least Squares Method

In this paper, least squares approximation method is developed for solving a class of linear fractional integro-differential equations comprising Volterra and Fredhlom cases. This method is based on a polynomial of degree n to compute an approximate solution of these equations. The convergence analysis of the proposed method is proved. In addition, to show the accuracy and the efficiency of the proposed method, some examples are presented