The Existence and Uniqueness of Mild Solutions for Fuzzy Hilfer Fractional Evolution Equations with Non-Local Conditions
Year: 2025
Type: article
Abstract: In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type 0<β<1 and order 1<α<2 subject to nonlocal conditions. Using the infinitesimal generator of a strongly continuous cosine family, we define a mild solution for the proposed system. The existence and uniqueness of such mild solutions are established through Schauder’s fixed-point theorem and the Banach contraction principle. An illustrative application to a fuzzy fractional wave equation is presented to demonstrate the effectiveness of the developed approach. The main contribution of this study lies in the unified treatment of fuzzy Hilfer fractional evolution equations under nonlocal conditions, which generalizes and extends several existing results and provides a solid analytical foundation for modeling systems with memory and uncertainty.
Source: Axioms
Authors: Kholoud N. Alharbi, Sanaa Alotaibi
Institutions: Qassim University, King Abdulaziz University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Funder: Qassim University
Award: G92618698
OpenAlex ID: W4416458407
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