An application to a system of (k,ρ)-fractional Hilfer integral equations via a measure of noncompactness

2025/12/26 by Gete Umbrey, Umbrey, Gete, Riken Kaye +7
Mathematics · #26A33 #47H08 #47H09 #47H10 #FOS: Mathematics #Fixed Point Theorems Analysis #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2512.22000

openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

In our study, Darbo's fixed point theorem(DFPT) has been extended and generalized using ℍ-class mappings and the measure of noncompactness. Utilizing this Darbo-type theorem, we provided a solvability result for a system of a (k,ρ)-fractional Hilfer integral equations, accompanied by an appropriate example to illustrate the findings.

Citations

• Regular measures of noncompactness and Ascoli-Arzel\` a type compactness criteria in spaces of vector-valued function
• Representation of measures of noncompactness and its applications related to an initial-value problem in Banach spaces

Related

• Properties of Some ψ-Hilfer fractional Integrodifferential equations
• On a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions
• Application of a generalization of Darbos fixed point theorem on an integral equation involving the weighted fractional integral with respect to another function
• Existence and Ulam-Hyers Mittag-Leffler stability of ψ-Hilfer fractional functional integrodifferential equation
• Existence and stability results for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions