Existence of Solutions for a Fractional Boundary Value Problem at Resonance

Abstract

In this paper, we focus on the existence of solutions to a fractional boundary value problem at resonance. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin.

On the Solutions of a Class of Nonlinear Fractional Differential Equations with Boundary Conditions

“…In this paper, we continue the study of a class of boundary value problems, using fractional derivative of Caputo of order α ∈ (2, 3). Following the results obtained in [14], it is presented a result of existence of solutions [14] and conditions are obtained to guarantee its uniqueness by applying the Banach contraction theorem. From a numerical point of view, it is considered the Adomian decomposition method, which provides a numerical approximation to the solution.…”

“…Continuing the results presented in [14], we consider the fractional boundary value problem with (left) Caputo fractional derivative (FBVP)…”