A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
Hojjat Afshari, Erdal Karapınar
Abstract
Abstract In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ -Hilfer fractional differential equations. For our purpose, we use the $\alpha -\psi $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> <mml:mo>−</mml:mo> <mml:mi>ψ</mml:mi> </mml:math> Geraghty-type contraction in the framework of the b -metric space. We give an example illustrating the validity of the proved results.
Topics & Concepts
MathematicsMetric spaceBoundary value problemPartial differential equationMetric (unit)Ordinary differential equationBoundary valuesFractional calculusApplied mathematicsMathematical analysisPure mathematicsDifferential equationOperations managementEconomicsFixed Point Theorems AnalysisNonlinear Differential Equations AnalysisFractional Differential Equations Solutions