Measures of noncompactness in the space of regulated functions R ( J , ℝ ∞ ) and its application to some nonlinear infinite systems of fractional differential equations

We study the following infinite systems of fractional boundary value problem: The goal of this paper is to bring forward a new measures of noncompactness in the space R ( J , ℝ ∞ ) consisting of all regulated functions, defined on the compact interval J ⊂ ℝ with values in ℝ ∞ and prove a fixed point theorem of Darbo-type in the Fréchet space R ( J , ℝ ∞ ) . Next, we formulate the Nemytskii operator to be acting from the space R ( J , ℝ ∞ ) into itself. Eventually, we demonstrate an example to which supports and usefulness of the obtained result.

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