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 xed point theorems, and the properties of the Mittag-Leer 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.
In this paper, a version modied of contraction Hardy-Rogers type in a metric space and is proved. Moreover, we apply this modied version to investigate the existence of unique solution of boundary value problems for the dierential equations and generalized fractional dierential equations through help of the properties of Green function. We also provide an example in support of acquired results. These results extend various comparable results from literature.
In this paper, some theorems concerning the existence and uniqueness of fixed point in complete metric space are established. The results of the continuity clause we reached are introduced and some of the results we obtained are circulated.
In this work, a new common fixed point result by generalized contractive functions fulfilling the type of admissibility condition in a Hausdorff Branciari metric space with the support of C-functions, was obtained.
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