Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative

Abdelhamid Mohammed Djaouti (), Zareen A. Khan (), Muhammad Imran Liaqat and Ashraf Al-Quran
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Abdelhamid Mohammed Djaouti: Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia
Zareen A. Khan: Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Muhammad Imran Liaqat: Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan
Ashraf Al-Quran: Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia

Mathematics, 2024, vol. 12, issue 7, 1-21

Abstract: In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in L p space by using Jensen’s, Grönwall–Bellman’s, Hölder’s, and Burkholder–Davis–Gundy’s inequalities, and the interval translation technique for a class of fractional neutral stochastic differential equations. We establish the results within the framework of the Ψ -Caputo derivative. We generalize the two situations of p = 2 and the Caputo derivative with the findings that we obtain. To help with the understanding of the theoretical results, we provide two applied examples at the end.

Keywords: fractional calculus; ?-Caputo derivative; neutral stochastic differential equations; existence and uniqueness; averaging principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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