Ulam‐Hyers‐Rassias stability for generalized fractional differential equations

Djalal Boucenna, Abdellatif Ben Makhlouf, El‐sayed El‐hady, Mohamed Ali Hammami

2021Mathematical Methods in the Applied Sciences13 citationsDOI

Abstract

In this paper, we present a generalized Gronwall inequality with singularity. Using this inequality, we investigate the existence, uniqueness, and Ulam‐Hyers‐Rassias stability for solutions of a class of generalized nonlinear fractional differential equations of order α (1 < α < 2). In this way, we improve and generalize several earlier outcomes.

Topics & Concepts

MathematicsUniquenessGronwall's inequalityStability (learning theory)Nonlinear systemSingularityClass (philosophy)Fractional calculusApplied mathematicsMathematical analysisInequalityPure mathematicsArtificial intelligencePhysicsQuantum mechanicsComputer scienceMachine learningFunctional Equations Stability ResultsFractional Differential Equations SolutionsNonlinear Differential Equations Analysis