Effects of the Caputo fractional derivatives on convective flow in wavy vented enclosures filled with a porous medium using Al 2 O 3 ‐Cu hybrid nanofluids

Heat Transfer ◽  
2020 ◽  
Vol 49 (4) ◽  
pp. 1895-1919
Author(s):  
Sameh E. Ahmed ◽  
Mohamed A. Mansour ◽  
Emad A.‐B. Abdel‐Salam ◽  
Eman F. Mohamed
Keyword(s):  
Porous Medium ◽  
Convective Flow ◽  
Fractional Derivatives ◽  
Caputo Fractional Derivatives ◽  
Hybrid Nanofluids ◽  
Vented Enclosures

Casson Model of MHD Flow of SA-Based Hybrid Nanofluid Using Caputo Time-Fractional Models

2019 ◽  
Vol 390 ◽  
pp. 83-90 ◽  
Author(s):  
Sidra Aman ◽  
Syazwani Mohd Zokri ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh ◽  
Ilyas Khan
Keyword(s):  
Fractional Derivatives ◽  
Volume Fraction ◽  
Vertical Channel ◽  
Mhd Flow ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Caputo Fractional Derivatives ◽  
Fractional Models ◽  
Hybrid Nanofluids ◽  
Time Fractional Derivative

In this paper MHD flow of Casson hybrid nanofluids are investigated with Caputo time-fractional derivative. Alumina (Al) and copper (Cu) are used as nanoparticles in this study with heat, mass transfer and MHD flow over a vertical channel in a porous medium. The problem is modeled using Caputo fractional derivatives and thermophysical properties of hybrid nanoparticles. The influence of concerned parameters is investigated physically and graphically on the heat, concentration and flow. The effect of volume fraction on thermal conductivity of hybrid nanofluids is observed.

scholarly journals Multiple Fractional Solutions for Magnetic Bio-Nanofluid Using Oldroyd-B Model in a Porous Medium with Ramped Wall Heating and Variable Velocity

2020 ◽  
Vol 10 (11) ◽  
pp. 3886 ◽  
Author(s):  
Muhammad Saqib ◽  
Ilyas Khan ◽  
Yu-Ming Chu ◽  
Ahmad Qushairi ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Porous Medium ◽  
Temperature Field ◽  
Velocity Field ◽  
Fractional Derivatives ◽  
Fluid Velocity ◽  
Fractional Operators ◽  
Caputo Fractional Derivatives ◽  
Wall Heating ◽  
The Laplace Transform ◽  
Fractional Analysis

Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid. Based on three different definitions of fractional operators, three different models of the resulting nanofluid are developed. These three operators are based on the definitions of Caputo (C), Caputo–Fabrizio (CF), and Atnagana–Baleanu in the Caputo sense (ABC). Nanofluid is taken over an upright plate with ramped wall heating and time-dependent fluid velocity at the sidewall. The effects of magnetohydrodynamic (MHD) and porous medium are also considered. Triple fractional analysis is performed to solve the resulting three models, based on three different fractional operators. The Laplace transform is applied to each problem separately, and Zakian’s numerical algorithm is used for the Laplace inversion. The solutions are presented in various graphs with physical arguments. Results are computed and shown in various plots. The empirical results indicate that, for ramped temperature, the temperature field is highest for the ABC derivative, followed by the CF and Caputo fractional derivatives. In contrast, for isothermal temperature, the temperature field of C-derivative is higher than the CF and ABC derivatives, respectively. It was noticed that the velocity field for the ABC derivative is higher than the CF and Caputo fractional derivatives for ramped velocity. However, the velocity field for the Caputo fractional derivative is lower than the ABC and CF for isothermal velocity.

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

scholarly journals Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Time Delay ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fractional Operator ◽  
Caputo Fractional Derivatives ◽  
Picard Operator

AbstractThis study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.

scholarly journals On resonant mixed Caputo fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Assia Guezane-Lakoud ◽  
Adem Kılıçman
Keyword(s):  
Differential Equation ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Caputo Fractional Derivatives ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Problem At Resonance

Abstract The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.

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