Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative

Abstract

Abstract. The purpose of this paper is to establish some types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit Hadamard fractional-order differential equation.Mathematics Subject Classification (2010): 26A33, 34A08.

Stability via successive approximation for nonlinear implicit fractional differential equations

“…Recently, Benchora et al [17,18,19] obtained existence and various kinds of Ulam-Hyers stabilities for nonlinear implicit fractional differential equations (NIFDEs) involving Caputo fractional derivative with initial and boundary conditions. Kucche et al [20,21] have studied existence, uniqueness, continuous dependence and other properties of solutions for NIFDEs .…”

Stability for impulsive implicit Hadamard fractional differential equations

“…In [1] the authors S Abbas, W Albarakati, M Benchohra, JJ Trujillo have considered the Ulam Stabilities for partial hadamard fractional integral equations by appliqueing the Schauder's fixed-point theorem. The reader to refer the papers of Benchohra et al [4,5], S. Abbas, M. Benchohra et al [2] and see [22,23,26,27].…”

Existence results and Hyers-Ulam stability to a class of nonlinear arbitrary order differential equations

“…However for non-integer order differential equations, the area has not yet properly explored and required further exploration. Recently very few articles on Hyers-Ulam stability for the solutions of differential equations of arbitrary order have been published which we refer in [3,4,7,24,25,27,31]. Motivated by the aforesaid work, this article is concerned to investigate existence and stability of solutions for fractional differential equations of arbitrary order which have boundary conditions involving fractional order derivative in the following form…”