10.57647/cna.2025.vgbv

A Study on the Existence and Local Attractivity of Solutions to Fractional Order Nonlinear Quadratic Functional Random Differential Equations via Fixed Point Theory

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  • Bhalchandra D. Karande1,
  • Kalpana D. Jagtap*2,
  1. Department of Mathematics, Maharashtra Udaygiri College, Udgir, India
  2. Department of Mathematics, Dayanand Science College, Latur, India

Received: 2025-10-30

Revised: 2025-11-18

Accepted: 2025-12-09

Published in Issue 2025-12-30

Copyright (c) 2025 Bhalchandra D. Karande, Kalpana D. Jagtap (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A Study on the Existence and Local Attractivity of Solutions to Fractional Order Nonlinear Quadratic Functional Random Differential Equations via Fixed Point Theory. (2025). Communications in Nonlinear Analysis, 13(2). https://doi.org/10.57647/cna.2025.vgbv

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Abstract

In this paper, we consider an initial value problem (IVP) for fractional order nonlinear quadratic functional random differential equation in a Banach algebra. The novelty of this work lies in the formulation and analysis of such an equation within the framework of Banach algebra under randomness, which has not been adequately addressed in the existing literature. Under appropriate fixed point theorem by using Caratheodory and Lipschitz conditions, a set of suitable hypotheses is formulated, and the existence of a random solution is established. Moreover, the local attractivity of the solution is proved. The results obtained in this study are useful for the qualitative analysis of complex dynamical systems with memory and random effects arising in applied sciences and engineering.

Keywords

  • Bernoulli polynomials,
  • Hypergeometric Bernoulli polynomials,
  • Integral representation,
  • Asymptotic formula,
  • Zero attractor
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