Solution of a fractal energy integral operator without body force using measure of noncompactness

Authors: Nguyễn Hữu Cần, Hemant Kumar Nashine, Rabha W. Ibrahim,

https://doi.org/10.1016/j.aej.2020.07.015

Publisher, magazine: ,

Publication year: 2020

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Abstract

In this paper, we study the solution of fractal energy integral equation for one-dimensional compressible flows without body force using measure of noncompactness. We also discuss the solution of the local fractal equation of losing energy system using the notion of local fractal differential idea. For this, a new notion of --set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.

Tags: Measure of noncompactness, Darbo fixed point theorem, Locally fractional calculus, Fractal integral equation, Energy