Upper and Lower Solution method for Positive solution of generalized Caputo fractional differential equations

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.

Keywords

• fractional differential equations,existence and upper and lower solutions,Mittag-Leffler function,generalized Laplace transform,fixed point theorems

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