Solvability of fractional dynamic systems utilizing measure of noncompactness

Nonlinear Analysis

Reza Arab¹  Mohsen Rabbani¹  Rabha W. Ibrahim²  Hemant Kumar Nashine³ 

[1] Islamic Azad University;Ton Duc Thang University;Vellore Institute of Technology;

关键词: fractional calculus;    fractional differential operator;    fixed point theorem;    measure of noncompactness;   

DOI  :  10.15388/namc.2020.25.17896

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown