Abstract
The existence of the mild solution to the impulsive integro-differential equation with a Conformable Fractional differential operator of order \(0<\gamma \le 1\) has been established in this article by considering both classical and non-local conditions. The idea of fixed point theorems, operator semigroups generated by the linear part of the equation, and nonlinear functional analysis are used to produce existence findings. We incorporated illustrations to validate our findings.
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Acknowledgements
Authors wish to acknowledge Department of Mathematics, National Institute of Technology Puducherry for organizing the International Conference on Fractional Calculus: Theory, Applications and Numerics and giving us opportunity to present research paper at the conference.
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HK contributed in critical revision of the manuscript and intellectual inputs and supervision of the research work; PP was responsible for conceptualization, analysis, interpretation of data, and original drafting of manuscript; VS for analysis as well as simultaneous drafting of manuscript; all authors read and approved final manuscript.
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Kataria, H.R., Patel, P.H. & Shah, V. Impulsive integro-differential systems involving conformable fractional derivative in Banach space. Int. J. Dynam. Control 12, 56–64 (2024). https://doi.org/10.1007/s40435-023-01224-3
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DOI: https://doi.org/10.1007/s40435-023-01224-3
Keywords
- Conformable factional integro-differential equation
- Impulsive conditions
- Operator semigroup
- Fixed point theorem