scholarly journals Non-Field Analytical Method for Filtration of Slightly Compressible Fluid through Porous Media with Stagnation Areas

2021 ◽  
Author(s):  
Vladimir Kulish ◽  
Michal Schmirler ◽  
Pavel Sláma
Keyword(s):  
Integral Equation ◽  
Porous Media ◽  
Compressible Fluid ◽  
Analytical Method ◽  
Integral Operators ◽  
Filtration Problem ◽  
Slightly Compressible ◽  
Unsteady Filtration ◽  
Fractional Orders ◽  
Pressure Evolution

Abstract In this study the method of Kulish has been used to derive a non-field solution of the equation, which models the process of unsteady filtration of a slightly compressible fluid within a domain consisting of both flow and stagnation areas under the influence of some pressure distribution at the boundary. The solution relates the local values of pressure and the corresponding pressure gradient and is valid everywhere within the domain including the boundary. The solution thus obtained is in the form of a series with respect to generalised differ-integral operators of fractional orders. The solution has been compared with the know solution of the filtration problem with no stagnation areas. Finally, an integral equation to estimate the pressure evolution at the boundary for a given filtration speed has been proposed.

scholarly journals Asymptotics of inverse filtration problem in porous media

2021 ◽  
Vol 1030 ◽  
pp. 012109
Author(s):  
Liudmila Kuzmina ◽  
Yuri Osipov ◽  
Victoria Tzariova
Keyword(s):  
Porous Media ◽  
Filtration Problem

A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media

2014 ◽  
Vol 26 (5) ◽  
pp. 053102 ◽  
Author(s):  
D. Lasseux ◽  
F. J. Valdes Parada ◽  
J. A. Ochoa Tapia ◽  
B. Goyeau
Keyword(s):  
Porous Media ◽  
Slip Flow ◽  
Macroscopic Model ◽  
Slightly Compressible ◽  
Homogeneous Porous Media ◽  
Compressible Gas

scholarly journals On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Havva Kavurmacı Önalan ◽  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Frequency Of Use ◽  
Second Derivatives ◽  
New Variant ◽  
Type Integral ◽  
Basic Concepts

AbstractThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

scholarly journals Convolution integral equation of Fredholm type with certain trancedental functions

2008 ◽  
Vol 39 (3) ◽  
pp. 227-237
Author(s):  
V. B. L. Chaurasia ◽  
Vishal Saxena
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Special Function ◽  
Integral Operators ◽  
Convolution Integral ◽  
Fredholm Type ◽  
Fractional Integral Operators ◽  
Convolution Integral Equation ◽  
Weyl Fractional Integral

The aim of this paper is to establish a solution of a certain class of convolution integral equation of Fredholm type whose kernel involve certain product of special function by using Riemann-Liouville and Weyl fractional integral operators. Some interesting particular cases are also considered.

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