Upper and Lower Solution method for Positive solution of generalized Caputo fractional differential equations
Jayshree PATİL, Archana CHAUDHARİ, Mohammed S. Abdo, Basel HARDAN
Abstract
In this research paper, the nonlinear fractional relaxation equation involving the generalized Caputo derivative is reduced to an equivalent integral equation via the generalized Laplace transform. Moreover, the upper and lower solutions method combined with some fixed point theorems, and the properties of the Mittag-Leffler function are applied to investigate the existence and uniqueness of positive solutions for the problem at hand. At the end, to illustrate our results, we give an example.
Topics & Concepts
UniquenessMathematicsLaplace transformFractional calculusRelaxation (psychology)Mathematical analysisMittag-Leffler functionFixed-point theoremNonlinear systemFunction (biology)Applied mathematicsPhysicsQuantum mechanicsBiologySocial psychologyEvolutionary biologyPsychologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems