An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation
Shahram Rezapour, Bouchra Azzaoui, Brahim Tellab, Sina Etemad, H. P. Masiha
Abstract
In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.
Topics & Concepts
MathematicsBoundary value problemFunction (biology)Mathematical analysisFixed-point theoremPoint (geometry)Initial value problemBoundary (topology)Value (mathematics)Boundary valuesGeometryEvolutionary biologyStatisticsBiologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems