Alexandria Engineering Journal

Alexandria Engineering Journal

Volume 59, Issue 6, December 2020, Pages 4101-4106
Alexandria Engineering Journal

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

https://doi.org/10.1016/j.aej.2020.07.015Get rights and content
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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 χ-Δ-set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.

Keywords

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

2010 MSC

47H08
47H10
47H09

Cited by (0)

Peer review under responsibility of Faculty of Engineering, Alexandria University.