Positive Solutions for FirstOrder Nonlinear CaputoHadamard Fractional Relaxation Differential Equations
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Authors: A. ARDJOUNI AND A. DJOUDI
DOI: 10.46793/KgJMat2106.897A
Abstract:
This article concerns the existence and uniqueness of positive solutions of the ﬁrstorder nonlinear CaputoHadamard fractional relaxation diﬀerential equation

where 0 < α ≤ 1. In the process we convert the given fractional diﬀerential equation into an equivalent integral equation. Then we construct appropriate mappings and employ the Krasnoselskii ﬁxed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach ﬁxed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.
Keywords:
Fixed points, fractional diﬀerential equations, positive solutions, existence, uniqueness, relaxation phenomenon.
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