Solvability of fractional dynamic systems utilizing measure of noncompactness
Articles
Hemant Kumar Nashine
Vellore Institute of Technology
Rabha W. Ibrahim
Ton Duc Thang University
https://orcid.org/0000-0001-9341-025X
Reza Arab
Islamic Azad University
https://orcid.org/0000-0002-3790-4703
Mohsen Rabbani
Islamic Azad University
https://orcid.org/0000-0003-3602-6125
Published 2020-07-01
https://doi.org/10.15388/namc.2020.25.17896
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Keywords

fractional calculus
fractional differential operator
fixed point theorem
measure of noncompactness

How to Cite

NashineH. K., IbrahimR. W., ArabR. and RabbaniM. (2020) “Solvability of fractional dynamic systems utilizing measure of noncompactness”, Nonlinear Analysis: Modelling and Control, 25(4), pp. 618–637. doi: 10.15388/namc.2020.25.17896.

Abstract

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. 

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