Fractional order nonlinear random differential equation in separable Banach algebra

Document Type : Research Paper

Authors

1 Department of Mathematics, Dayanad Science College, Latur

2 Department of Mathematics, Maharashtra Udaygiri Mahavidyalaya, Udgir (413517).

Abstract

This paper investigates fractional-order differential equations with random operators in a separable Banach algebra. The main goal is to prove the existence of random solutions for these equations. We focus on an initial value problem involving fractional order differential equations with random operators. By transforming this initial value problem into an
equivalent integral form and applying the fixed point theorem along with the Caratheodory condition, we formulate some hypothesis for the existence of random solutions. Additionally, we demonstrate that these random solutions possess local attractivity. This study provides a framework for understanding and solving existence of random solutions for fractional order differential equations with random operators. An illustrative example is also provided to verify and demonstrate the applicability of the main result.

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References

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Journal of Hyperstructures
Volume 15, Issue 1
June 2026
Pages 112-122

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