Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations

Sumbel Shahid ^[1] ; Shahid Saifullah ^[1] ; Usman Riaz ^[2] ; Akbar Zada ^[1] ; Sana Ben Moussa ^[3]
1. [1] University of Peshawar
  
  University of Peshawar
  
  Pakistán
2. [2] Qurtuba University of Science and Information Technology
  
  Qurtuba University of Science and Information Technology
  
  Pakistán
3. [3] King Khalid University
  
  King Khalid University
  
  Arabia Saudí
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
Idioma: inglés
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Resumen
- In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theorems, respectively. Uniqueness and at least one solution of corresponding coupled form of the proposed nonlinear system will be prove through Banach contraction theorem and Arzela–Ascoli theorem, respectively. ` Under some hypothesis, we scrutinize Hyers–Ulam stability of the mentioned nonlinear equation and its corresponding coupled nonlinear system. For the support of our main results, we present examples.