Existence of Mild Solutions for Multi-Term Time-Fractional Random Integro-Differential Equations with Random Carathéodory Conditions

In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure o...

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Bibliographic Details
Published in:Axioms 2021-12, Vol.10 (4), p.252
Main Authors: Diop, Amadou, Du, Wei-Shih
Format: Article
Language:English
Subjects:
Banach spaces
Calculus
Carathéodory condition
Differential equations
Fixed points (mathematics)
measure of noncompactness
multi-term fractional differential equation
Mönch’s fixed point theorem
random effect
random operator
Random variables
Stochastic models
Theorems
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Summary:In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure of noncompactness and resolvent family theory. Under the condition that the nonlinear term is of Carathéodory type and satisfies some weakly compactness condition, we establish the existence of random mild solutions. A nontrivial example illustrating our main result is also given.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10040252