A fixed point theorem for Hardy-Rogers type on generalized fractional differential equations

Abstract

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.

Fixed Point Results for Almost Contraction Mappings in Fuzzy Metric Space

“…established unified Fp theorems in 𝐹ℳ-spaces. Further significant results on the Fp within the 𝐹ℳ-spaces may be seen in [12][13][14] .…”

Modify Conditions of Hardy-Rogers' Fixed Point Theorem

“…Recently, many researchers have extensively studied these types of fixed point theorems ( [4][5][6][7][8], [12][13][14][15]). Many of the concepts have been introduced recently in the Hardy-Rogers theory from those studies we mention, Rangamma [16] proved Hardy and Rogers type common fixed point theorem for a family of self-maps in cone 2-metric spaces, in the same way.…”