scholarly journals Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative

2020 ◽  
Vol 5 (2) ◽  
pp. 1062-1073 ◽  
Author(s):  
Ritu Agarwal ◽  
◽  
Mahaveer Prasad Yadav ◽  
Dumitru Baleanu ◽  
S. D. Purohit ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Flow Equation ◽  
Miscible Flow

scholarly journals Analytical solution for fractional derivative gas-flow equation in porous media

2017 ◽  
Vol 7 ◽  
pp. 2432-2438 ◽  
Author(s):  
Mohamed F. El Amin ◽  
Ahmed G. Radwan ◽  
Shuyu Sun
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Gas Flow ◽  
Flow Equation

Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Akbar Zada
Keyword(s):  
Fractional Derivative ◽  
Positive Solutions ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Relaxation Equation ◽  
Monotone Iterative ◽  
Banach Contraction ◽  
Uniqueness Of The Solution ◽  
Fractional Relaxation ◽  
The Banach Contraction Principle

Abstract This manuscript is committed to deal with the existence and uniqueness of positive solutions for fractional relaxation equation involving ψ-Caputo fractional derivative. The existence of solution is carried out with the help of Schauder’s fixed point theorem, while the uniqueness of the solution is obtained by applying the Banach contraction principle, along with Bielecki type norm. Moreover, two explicit monotone iterative sequences are constructed for the approximation of the extreme positive solutions to the proposed problem. Lastly, two examples are presented to support the obtained results.

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

scholarly journals Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Fathalla A. Rihan ◽  
Chinnathambi Rajivganthi ◽  
Palanisamy Muthukumar
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Poisson Jumps ◽  
Hilfer Fractional Derivative ◽  
Analysis Techniques ◽  
Mild Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Existence Of Optimal Control

In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

scholarly journals Studying the fractional derivative for natural convection in slanted cavity containing porous media

2019 ◽  
Vol 1 (9) ◽  
Author(s):  
Sameh E. Ahmed ◽  
M. A. Mansour ◽  
E. A-B. Abdel-Salam ◽  
Eman F. Mohamed
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Fractional Derivative
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