Fractional integro-differential equations arise in the mathematical modelling of various physical phenomena like heat conduction in materials with memory, diffusion processes etc. In this paper, we have taken the fractional integro-differential equation of type Dy(t) = a(t)y(t) + f(t) + ∫ t

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

In this paper, a new numerical method for solving a linear system of fractional integro-differential equations is presented. The fractional derivative is considered in the Caputo sense. The proposed technique is based on the new operational matrices of triangular functions. The suggested method reduces this type of system to the solution of system of linear algebraic equations. To demonstrate t...

Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...

The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

Correspondence: [email protected] Department of Mathematics, Faculty of Science, Guelma University Guelma, Algeria Abstract In this article, sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus, resolvent operators, and ...