Qualitative analysis of nonlinear implicit neutral differential equation of fractional order

Qualitative analysis of nonlinear implicit neutral differential equation of fractional order

In this paper, we discuss sufficient conditions for the existence of solutions for a class of Initial value problem for an neutral differential equation involving Caputo fractional derivatives. Also, we discuss some types of Ulam stability for this class of implicit fractional-order differential equ...

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Bibliographic Details
Published in:AIMS mathematics Vol. 6; no. 4; pp. 3703 - 3719
Main Authors: Hashem, H. H. G., Alrashidi, Hessah O.
Format: Journal Article
Language:English
Published: AIMS Press 01-01-2021
Subjects:
attractivity of solutions
caputo fractional derivative
mild solution
neutral differential equation
ulam stability
ulam-hyers stability
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Summary:In this paper, we discuss sufficient conditions for the existence of solutions for a class of Initial value problem for an neutral differential equation involving Caputo fractional derivatives. Also, we discuss some types of Ulam stability for this class of implicit fractional-order differential equation. Some applications and particular cases are presented. Finally, the existence of at least one mild solution for this class of implicit fractional-order differential equation on an infinite interval by applying Schauder fixed point theorem and the local attractivity of solutions are proved.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021220