Boundary value problems of Hilfer-type fractional integro-differential equations and inclusions with nonlocal integro-multipoint boundary conditions
Cholticha Nuchpong, Sotiris K. Ntouyas, Jessada Tariboon
Abstract
Abstract In this paper, we study boundary value problems of fractional integro-differential equations and inclusions involving Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray-Schauder in the single-valued case, while Martelli’s fixed point theorem, nonlinear alternative for multi-valued maps, and Covitz-Nadler fixed point theorem are used in the inclusion case. Examples illustrating the obtained results are also presented.
Topics & Concepts
MathematicsFixed-point theoremMathematical analysisBoundary value problemUniquenessFractional calculusType (biology)Picard–Lindelöf theoremSchauder fixed point theoremNonlinear systemBiologyPhysicsQuantum mechanicsEcologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems