Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ−Caputo Fractional Boundary Value Problem
Abdelatif Boutiara, Maamar Benbachir, Jehad Alzabut, Mohammad Esmael Samei
Abstract
The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ. Our main results are obtained by applying the monotone iterative technique combined with the method of upper and lower solutions. Further, we consider three cases for ψ*(t) as t, Caputo, 2t, t, and Katugampola (for ρ=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.
Topics & Concepts
Monotone polygonMathematicsNonlinear systemBoundary value problemFractional calculusValue (mathematics)Iterative methodApplied mathematicsDerivative (finance)Mathematical analysisMathematical optimizationGeometryStatisticsPhysicsFinancial economicsEconomicsQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods