Generalized weakly singular Gronwall-type inequalities and their applications to fractional differential equations
Minh Dien Nguyen
Abstract
We propose and prove some new generalized Gronwall-type inequalities with respect to an appropriate function ψ. We consider the integral inequalities including not only one integral but also two integrals with doubly singular kernels. We apply these inequalities to study the existence and stability of solution of fractional differential equations with weakly singular sources.
Topics & Concepts
MathematicsGronwall's inequalityType (biology)InequalityStability (learning theory)Mathematical analysisSingular integralFunction (biology)Applied mathematicsDifferential equationDifferential (mechanical device)Integral equationComputer scienceMachine learningBiologyEngineeringEvolutionary biologyAerospace engineeringEcologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems