Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions
Nawapol Phuangthong, Sotiris K. Ntouyas, Jessada Tariboon, Kamsing Nonlaopon
Abstract
In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the 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, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results.
Topics & Concepts
MathematicsFixed-point theoremUniquenessBoundary value problemMathematical analysisPicard–Lindelöf theoremFractional calculusType (biology)Nonlinear systemSchauder fixed point theoremFixed pointApplied mathematicsPhysicsQuantum mechanicsEcologyBiologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFixed Point Theorems Analysis