New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions

K. Kaliraj, M. Manjula and C. Ravichandran

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: In this article, we examine a nonlinear impulsive neutral fractional differential equation with nonlocal condition in an arbitrary Hilbert space. We obtain an associated integral equation and then consider a sequence of approximate integral equations by the projection of considered associated nonlocal neutral fractional integral equation onto finite dimensional space. The existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed-point method are demonstrated. Convergence of the solutions of the approximate integral equation is proved. The Faedo-Galerkin approximation of the solution is studied and demonstrated some convergence results. Lastly, the application is presented to illustrate the theory of the main results.

Keywords: Neutral fractional differential equation; Analytic semigroup; Fixed-point theorem; Nonlocal conditions; Faedo-Galerkin approximation; Impulsive condition (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922004945

DOI: 10.1016/j.chaos.2022.112284

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