Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces

Ahmed Morsy; Kottakkaran Sooppy Nisar; Chokkalingam Ravichandran; Chandran Anusha; Ahmed Morsy; Kottakkaran Sooppy Nisar; Chokkalingam Ravichandran; Chandran Anusha

doi:10.3934/math.2023299

AIMS Mathematics

2023, Volume 8, Issue 3: 5934-5949. doi: 10.3934/math.2023299

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Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces

1.
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
2.
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India

Received: 05 November 2022 Revised: 08 December 2022 Accepted: 19 December 2022 Published: 27 December 2022
MSC : 34K40, 34K42

In this work, we scrutinize the existence and uniqueness of the solution to the Integro differential equations for the Caputo fractional derivative on the time scale. We derive the solution of the neutral fractional differential equations along the finite delay conditions. The fixed point theory is demonstrated, and the solution depends upon the fixed point theorems: Banach contraction principle, nonlinear alternative for Leray-Schauder type, and Krasnoselskii fixed point theorem.
- Neutral differential equations,
- fixed point,
- Caputo fractional derivative,
- time scales,
- Semigroup theory,
- delay differential equations
Citation: Ahmed Morsy, Kottakkaran Sooppy Nisar, Chokkalingam Ravichandran, Chandran Anusha. Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces[J]. AIMS Mathematics, 2023, 8(3): 5934-5949. doi: 10.3934/math.2023299

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Abstract

In this work, we scrutinize the existence and uniqueness of the solution to the Integro differential equations for the Caputo fractional derivative on the time scale. We derive the solution of the neutral fractional differential equations along the finite delay conditions. The fixed point theory is demonstrated, and the solution depends upon the fixed point theorems: Banach contraction principle, nonlinear alternative for Leray-Schauder type, and Krasnoselskii fixed point theorem.

References

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