Fuzzy neutral fractional integro-differential equation existence and stability results involving the Caputo fractional generalized Hukuhara derivative

Aziz El Ghazouani, Fouad Ibrahim Abdou Amir, M’hamed Elomari, Saïd Melliani

2024Journal of Nonlinear Complex and Data Science13 citationsDOI

Abstract

Abstract In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.

Topics & Concepts

UniquenessMathematicsStability (learning theory)Fractional calculusBanach spaceApplied mathematicsDifferential equationFuzzy logicDerivative (finance)Fixed-point theoremMathematical analysisComputer scienceFinancial economicsEconomicsMachine learningArtificial intelligenceFuzzy Systems and OptimizationNonlinear Differential Equations AnalysisFunctional Equations Stability Results