This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general natu...

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in thei...

Fractional calculus is at this time an area where many models are still being developed, explored, and used in real-world applications branches of science engineering non-locality plays a key role. Although wonderful discoveries have already been reported by researchers important monographs review articles, there great deal non-local phenomena that not studied only waiting to be explored. As re...

This article presents the analytical study of three species fractional food web model in framework Modified Caputo–Fabrizio operator. With help fixed point theory, existence and uniqueness results are investigated for order model. To obtain approximate solution suggested model, well-known Laplace–Adomian decomposition method is used. The solutions validated through simulations with a variety or...

In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α ∈ (1, 2) with a zero Dirichlet boundary condition.

In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

In this article, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative.