On the Analytical Treatment for the Fractional-Order Coupled Partial Differential Equations via Fixed Point Formulation and Generalized Fractional Derivative Operators

The analytical solutions for Volterra integro-differential equations within Local fractional operators by Yang-Laplace transform

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 ...

Numerical and Analytical Treatment of Differential Equations of Fractional Order

Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by { −D1 0+ y1(t) = λ1a1(t)f(t, y1(t), y2(t)) + e1(t), −D2 0+ y2(t) = λ2a2(t)g(t, y1(t), y2(t)) + e2(t), where ν1, ν2 ∈ (n− 1, n] for n > 3 and n ∈ N , subject to the boundary conditions y 1 (0) = 0 = y (i) 2 (0), for 0 ≤ ...

Existence results for hybrid fractional differential equations with Hilfer fractional derivative

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.