Boundary value problems for Hilfer type sequential fractional differential equations and inclusions involving Riemann–Stieltjes integral multi-strip boundary conditions
Cholticha Nuchpong, Sotiris K. Ntouyas, Ayub Samadi, Jessada Tariboon
Abstract
Abstract In this paper, we study boundary value problems for sequential fractional differential equations and inclusions involving Hilfer fractional derivatives, supplemented with Riemann–Stieltjes integral multi-strip boundary conditions. Existence and uniqueness results are obtained in the single-valued case by using the classical Banach and Krasnosel’skiĭ fixed point theorems and the Leray–Schauder nonlinear alternative. In the multi-valued case an existence result is proved by using nonlinear alternative for contractive maps. Examples illustrating our results are also presented.
Topics & Concepts
MathematicsMathematical analysisBoundary value problemRiemann–Stieltjes integralUniquenessNonlinear systemOrdinary differential equationFixed-point theoremType (biology)Partial differential equationFractional calculusIntegral equationDifferential equationBiologyEcologyPhysicsQuantum mechanicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFixed Point Theorems Analysis