10.1007/s40096-022-00489-7

Application of fixed point theorem on the study of the existence of solutions in some fractional stochastic functional integral equations

  • Manochehr Kazemi1,
  • Amar Deep2,
  • Alireza Yaghoobnia*3,
  1. Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, IR
  2. Mathematics Discipline, PDPM, Indian Institute of Information Technology Design and Manufacturing, Jabalpur, MP, IN
  3. Department of mathematics, Lahijan Branch, Islamic Azad University, Lahijan, IR

Published in Issue 2022-09-16

How to Cite

Kazemi, M., Deep, A., & Yaghoobnia, A. (2022). Application of fixed point theorem on the study of the existence of solutions in some fractional stochastic functional integral equations. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00489-7
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Abstract

Abstract In this paper, the conditions for the existence of a solution for fractional stochastic functional integral in Banach space are investigated. For this purpose, the concept of noncompactness measurement and Petryshyn’s fixed point theorem have been done to achieve the desired result. In general, any phenomenon that encounters some kind of instability or is related to a stochastic process is expressed and studied in the stochastic integral equations form. Also, by providing various applications and examples, the efficiency of the method on such equations is discussed.

Keywords

  • Fractional stochastic functional integral equations,
  • Existence of solution,
  • Measures of noncompactness,
  • Fixed point theorem

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