Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann−Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.