AI-driven controllability analysis of fractional impulsive neutral Volterra-Fredholm integro-differential equations with state-dependent delay

Prabakaran Raghavendran; Tharmalingam Gunasekar; Irshad Ayoob; Nabil Mlaiki; Prabakaran Raghavendran; Tharmalingam Gunasekar; Irshad Ayoob; Nabil Mlaiki

doi:10.3934/math.2025432

AIMS Mathematics

2025, Volume 10, Issue 4: 9342-9368. doi: 10.3934/math.2025432

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AI-driven controllability analysis of fractional impulsive neutral Volterra-Fredholm integro-differential equations with state-dependent delay

1.
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India
2.
Department of Mathematics, Institute of Engineering and Technology, Srinivas University, Mukka, Mangaluru, Karnataka 574146, India
3.
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia

Received: 01 February 2025 Revised: 08 April 2025 Accepted: 18 April 2025 Published: 23 April 2025
MSC : 34A08, 45J05, 65L20, 93C23, 68T07

This paper examined the controllability of fractional impulsive neutral Volterra-Fredholm integro-differential equations with state-dependent delay, employing the Caputo fractional derivative and a semigroup of compact and analytic operators. Controllability results were established by using Schauder's fixed point theorem, addressing the complexities arising from fractional dynamics combined with state-dependent delays. The theoretical findings were further confirmed through a detailed example and numerical simulations that show convergence of the solutions. Also, the role of artificial intelligence in the analysis and control of such systems governed by these equations was investigated, thereby opening up opportunities for machine learning to be coupled with fractional calculus for a better predictive solution and better control of systems. These results provide some insight into stability as well as controllability of systems governed by fractional differential equations with impulsive and state-dependent behaviors.
- Caputo fractional derivative,
- Schauder's fixed point theorem,
- controllability,
- artificial intelligence,
- system control
Citation: Prabakaran Raghavendran, Tharmalingam Gunasekar, Irshad Ayoob, Nabil Mlaiki. AI-driven controllability analysis of fractional impulsive neutral Volterra-Fredholm integro-differential equations with state-dependent delay[J]. AIMS Mathematics, 2025, 10(4): 9342-9368. doi: 10.3934/math.2025432

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Abstract

This paper examined the controllability of fractional impulsive neutral Volterra-Fredholm integro-differential equations with state-dependent delay, employing the Caputo fractional derivative and a semigroup of compact and analytic operators. Controllability results were established by using Schauder's fixed point theorem, addressing the complexities arising from fractional dynamics combined with state-dependent delays. The theoretical findings were further confirmed through a detailed example and numerical simulations that show convergence of the solutions. Also, the role of artificial intelligence in the analysis and control of such systems governed by these equations was investigated, thereby opening up opportunities for machine learning to be coupled with fractional calculus for a better predictive solution and better control of systems. These results provide some insight into stability as well as controllability of systems governed by fractional differential equations with impulsive and state-dependent behaviors.

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