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Open AccessArticle

Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

1
Department of Applied Mathematics, Virginia Military Institute (VMI), 431, Mallory Hall, Lexington, VA 24450, USA
2
PG and Research Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India
3
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India
4
Department of Mathematics, SRMV College of Arts and Science, Coimbatore 641020, Tamilnadu, India
*
Author to whom correspondence should be addressed.
Appl. Syst. Innov. 2019, 2(2), 18; https://doi.org/10.3390/asi2020018
Received: 24 October 2018 / Revised: 24 May 2019 / Accepted: 27 May 2019 / Published: 14 June 2019
(This article belongs to the Special Issue Non-linear Devices, Systems, Networks and Their Applications)
In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory. View Full-Text
Keywords: fractional differential equations; impulse; integro-differential equations; non local conditions; fixed point theorem fractional differential equations; impulse; integro-differential equations; non local conditions; fixed point theorem
MDPI and ACS Style

Chalishajar, D.; Ravichandran, C.; Dhanalakshmi, S.; Murugesu, R. Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces. Appl. Syst. Innov. 2019, 2, 18.

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