Existence and stability results for nonlinear implicit neutral fractional differential equations with finite delay and impulses. (English) Zbl 1358.34088

Benchohra, Mouffak; Bouriah, Soufyane; Henderson, Johnny

Commun. Appl. Nonlinear Anal. 22, No. 1, 46-67 (2015).

Summary: In this paper, we establish the existence and uniqueness of solutions for a class of nonlinear implicit neutral fractional differential equations with impulse. Also, the Ulam stability for such a class of problems will be considered. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem. We present an example to show the applicability of our results.

MSC:

34K37	Functional-differential equations with fractional derivatives
34K32	Implicit functional-differential equations
34K40	Neutral functional-differential equations
34K45	Functional-differential equations with impulses

Keywords:

Caputo’s fractional derivative; implicit fractional differential equations; existence; stability; fixed point