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Solvability of fractional dynamic systems utilizing measure of noncompactness
, R.W. Ibrahim, R. Arab, M. Rabbani
Published in Vilnius University Press
Volume: 25
Issue: 4
Pages: 618 - 637
Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in ℝn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large. © 2020 Authors. Published by Vilnius University Press.
About the journal
JournalNonlinear Analysis: Modelling and Control
PublisherVilnius University Press