Stability of impulsive fractional stochastic integro-differential equations with state dependent delay and Poisson jumps by using Mainardi’s function

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 15، Issue 1 - شماره پیاپی 32، خرداد 2025، صفحه 220-254   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87562.1423

نویسندگان

C. Mattuvarkuzhali^* ؛ I. Silambarasan

Department of Mathematics, Veltech Multitech Dr Rangarajan Dr. Sakunthala Engi-neering college,Avadi - 6000062, Tamil Nadu, India.

چکیده

In this work, the stability results for a nonlinear mathematical model are derived, and the power system is realized by utilizing fractional calculus theory. The fixed point theorem is used to establish sufficient conditions for the existence of a mild solution and the stability of a nonlinear impul-sive fractional stochastic integro-differential equation with state-dependent delays with Mainardi’s function in a Hilbert space. Numerical simulations are provided to validate the obtained theoretical results. The proposed model supports (i) predicting the instability of synchronization between generators and the lines and (ii) stabilizing the disturbance that occurs in synchronization among generators and the lines.

کلیدواژه‌ها

Fractional integro-differential equation؛ State dependent delay؛ Mild solution؛ Stability analysis؛ Stochastic calculus

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