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Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

Abdelkrim Salım, Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg

2020Advances in Difference Equations79 citationsDOIOpen Access PDF

Abstract

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

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MathematicsOrdinary differential equationC0-semigroupFixed-point theoremMathematical analysisBanach spaceNonlinear systemStability (learning theory)Type (biology)Measure (data warehouse)Boundary value problemPartial differential equationClass (philosophy)Applied mathematicsDifferential equationBiologyQuantum mechanicsPhysicsEcologyDatabaseArtificial intelligenceMachine learningComputer scienceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFixed Point Theorems Analysis