scholarly journals Thermal analysis of magnetohydrodynamic viscous fluid with innovative fractional derivative

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 351-359
Author(s):  
Mushtaq Ahmad ◽  
Muhammad Imran ◽  
Dumitru Baleanu ◽  
Ali Alshomrani
Keyword(s):  
Heat Transfer ◽  
Viscous Fluid ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Field Variable ◽  
Physical Parameters ◽  
Caputo Fractional Derivatives ◽  
Moving Plate ◽  
Respective Field ◽  
Energy And Momentum

In this study, an attempt is made to investigate a fractional model of unsteady and an incompressible MHD viscous fluid with heat transfer. The fluid is lying over a vertical and moving plate in its own plane. The problem is modeled by using the constant proportional Caputo fractional derivatives with suitable boundary conditions. The non-dimensional governing equations of problem have been solved analytically with the help of Laplace transform techniques and explicit expressions for respective field variable are obtained. The transformed solutions for energy and momentum balances are appeared in terms of series form. The analytical results regarding velocity and temperature are plotted graphically by MATHCAD software to see the influence of physical parameters. Some graphic comparisons are also mad among present results with hybrid fractional derivatives and the published results that have been obtained by Caputo. It is found that the velocity and temperature with constant proportional Capu?to fractional derivative are portrait better decay than velocities and temperatures that obtained with Caputo and Caputo-Fabrizio derivative. Further, rate of heat transfer and skin friction can be enhanced with smaller values of fractional parameter.

scholarly journals Thermal analysis of magnetohydrodynamic viscous fluid with innovative fractional derivative

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 351-359
Author(s):  
Mushtaq Ahmad ◽  
Muhammad Imran ◽  
Dumitru Baleanu ◽  
Ali Alshomrani
Keyword(s):  
Heat Transfer ◽  
Viscous Fluid ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Field Variable ◽  
Physical Parameters ◽  
Caputo Fractional Derivatives ◽  
Moving Plate ◽  
Respective Field ◽  
Energy And Momentum

In this study, an attempt is made to investigate a fractional model of unsteady and an incompressible MHD viscous fluid with heat transfer. The fluid is lying over a vertical and moving plate in its own plane. The problem is modeled by using the constant proportional Caputo fractional derivatives with suitable boundary conditions. The non-dimensional governing equations of problem have been solved analytically with the help of Laplace transform techniques and explicit expressions for respective field variable are obtained. The transformed solutions for energy and momentum balances are appeared in terms of series form. The analytical results regarding velocity and temperature are plotted graphically by MATHCAD software to see the influence of physical parameters. Some graphic comparisons are also mad among present results with hybrid fractional derivatives and the published results that have been obtained by Caputo. It is found that the velocity and temperature with constant proportional Capu?to fractional derivative are portrait better decay than velocities and temperatures that obtained with Caputo and Caputo-Fabrizio derivative. Further, rate of heat transfer and skin friction can be enhanced with smaller values of fractional parameter.

scholarly journals Dispersion of metallic/ceramic matrix nanocomposite material through porous surfaces in magnetized hybrid nanofluids flow with shape and size effects

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Zubair Akbar Qureshi ◽  
S. Bilal ◽  
M. Y. Malik ◽  
Qadeer Raza ◽  
El-Sayed M. Sherif ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Viscous Fluid ◽  
Metallic Matrix ◽  
Ceramic Matrix ◽  
Physical Parameters ◽  
Viscous Fluid Flow ◽  
Hybrid Nanofluids ◽  
Matrix Nanocomposites ◽  
Matrix Nanocomposite

AbstractMatrix nanocomposites are high performance materials possessing unusual features along with unique design possibilities. Due to extraordinary thermophysical characteristic contained by these matrix nanocomposites materials they are useful in several areas ranging from packaging to biomedical applications. Being an environment friendly, utilization of nanocomposites offer new technological opportunities for several sectors of aerospace, automotive, electronics and biotechnology. In this regards, current pagination is devoted to analyze thermal features of viscous fluid flow between orthogonally rotating disks with inclusion of metallic matrix nanocomposite (MMNC) and ceramic matrix nanocomposites (CMNC) materials. Morphological aspects of these nanomaterials on flow and heat transfer characteristics has been investigated on hybrid viscous fluid flow. Mathematical structuring of problem along with empirical relations for nanocomposites materials are formulated in the form of partial differential equations and later on converted into ordinary differential expressions by using suitable variables. Solution of constructed coupled differential system is found by collaboration of Runge–Kutta and shooting methods. Variation in skin friction coefficient at lower and upper walls of disks along with measurement about heat transfer rate are calculated against governing physical parameters. Impact of flow concerning variables on axial, radial components of velocity and temperature distribution are also evaluated. Contour plots are also drawn to explore heat and thermal profiles. Comparison and critical analysis of MMNc and CMNc have been presented at lower and upper porous disks. Our computed analysis indicates that hybrid nanofluids show significant influence as compared to simple nanofluids with the permutation of the different shape factors.

scholarly journals On Some Inequalities Involving Liouville–Caputo Fractional Derivatives and Applications to Special Means of Real Numbers

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 193 ◽  
Author(s):  
Bessem Samet ◽  
Hassen Aydi
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Real Numbers ◽  
Caputo Fractional Derivatives ◽  
Parallel Development ◽  
Special Means ◽  
The Right ◽  
Class Of Functions

We are concerned with the class of functions f ∈ C 1 ( [ a , b ] ; R ) , a , b ∈ R , a < b , such that c D a α f is convex or c D b α f is convex, where 0 < α < 1 , c D a α f is the left-side Liouville–Caputo fractional derivative of order α of f and c D b α f is the right-side Liouville–Caputo fractional derivative of order α of f. Some extensions of Dragomir–Agarwal inequality to this class of functions are obtained. A parallel development is made for the class of functions f ∈ C 1 ( [ a , b ] ; R ) such that c D a α f is concave or c D b α f is concave. Next, an application to special means of real numbers is provided.

A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050070 ◽  
Author(s):  
CONG WU
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Comparison Principle ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Order Systems ◽  
Caputo Fractional Derivatives ◽  
Full Result

In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

scholarly journals Caputo Fractional Derivative Hadamard Inequalities for Stronglym-Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xue Feng ◽  
Baolin Feng ◽  
Ghulam Farid ◽  
Sidra Bibi ◽  
Qi Xiaoyan ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Caputo Fractional Derivatives ◽  
Hadamard Inequality ◽  
Error Estimations ◽  
Better Than

In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and stronglym-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities form-convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature.

Non-uniform nanoparticle concentration effects on moving plate boundary layer

2016 ◽  
Vol 94 (11) ◽  
pp. 1222-1227 ◽  
Author(s):  
A. Mehmood ◽  
M. Usman
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Plate Boundary ◽  
Convective Transport ◽  
Physical Parameters ◽  
Nanoparticle Concentration ◽  
Concentration Effects ◽  
Moving Plate ◽  
Layer Flow

The inclusion of small nano-sized particles in a pure fluid changes the material properties of the resulting mixture, called a nanofluid, significantly. To understand the role of material particles on the convection process one needs an efficient modeling of the nanofluid. The homogeneous modeling is observed to underpredict the rate of heat transfer. This fact motivates the utilization of non-homogeneous modeling. In this study we considered the classical Sakiadis moving plate boundary layer flow of a nanofluid. Non-homogeneous concentration, which is a consequence of convective transport of nanoparticles within the boundary layer, has been utilized to calculate the heat transfer enhancement. Effects of different physical parameters have been investigated on the expedition of heat transfer phenomena. It is noted that significant increase in the rate of heat transfer is observed when the nanoparticle concentration is non-uniform across the boundary layer.

scholarly journals Construction of Functions for Fractional Derivatives using Matlab

2021 ◽  
pp. 1-10
Author(s):  
Olagunju Adeyemi Sunday ◽  
Joseph Folake Lois
Keyword(s):  
Fractional Derivative ◽  
Taylor Series ◽  
Fractional Derivatives ◽  
Polynomial Function ◽  
Taylor Series Expansion ◽  
Caputo Fractional Derivatives ◽  
Current Increase ◽  
Programming Tool ◽  
Comparative Review ◽  
High Level

MATLAB is a high level programming tool for technical computing, its application cuts across different sphere of science, engineering, finance, communication, music etc. With the current increase in the use of non-integer order derivatives, there is a need to have tools that handle them for effective applications. In this paper, we present a brief comparative review of 2 expressions of fractional derivative. MATLAB functions for approximating Riemann-Liouville and Caputo fractional derivatives are presented alongside. Numerical simulations with test examples are implemented and results compared. To effectively handle non-polynomial function, Taylor series expansion is employed to convert the function into a form that can be easily handled.

scholarly journals Estimates of Mean-Type Fractional Inequalities For Differentiable Functions

2021 ◽  
Author(s):  
Muhammad Samraiz ◽  
Zahida Perveen ◽  
Sajid Iqbal ◽  
Saima Naheed ◽  
Thabet Abdeljawad
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Hilfer Fractional Derivative ◽  
Caputo Fractional Derivatives ◽  
Differentiable Functions ◽  
Wide Range ◽  
Type Integral ◽  
Special Case

In this article, we established a wide range of fractional mean-type integral inequalities for notable Hilfer fractional derivative using twice differentiable convex and $s$-convex functions for $s\in(0,1]$ with related identities. Also the results for Caputo fractional derivatives are derived as a special case of our general results.

scholarly journals Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xiying Wang ◽  
Wenfeng Wang ◽  
Yuanxiao Li
Keyword(s):  
Drug Treatment ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Threshold Value ◽  
Critical Threshold ◽  
Future Research ◽  
Caputo Fractional Derivatives ◽  
Hereditary Effects ◽  
Hiv Aids

In this paper, we formulate and investigate new switched HIV/AIDS models with drug treatment involving Caputo-fractional derivatives. Initially, due to the fractional derivative order related to the memory and hereditary effects and supposing that the model coefficients are time-varying parameters, we develop a Caputo-fractional order HIV/AIDS models with switching parameters and study their dynamics utilizing Lyapunov–Razumikhin technique. Furthermore, the results show that the fractional derivative α ( 0 < α < 1 ) and the switching parameters are related to the critical threshold value ( R ^ or R ¯ ) which ensures disease eradication under the condition of R ^ < 1 or R ¯ < 1 . Then, a treatment compartment is introduced into the above model from the asymptomatic infected individuals until the full blown AIDS individuals. Novel sufficient conditions on the threshold value are derived to verify that the disease is eventually cleared as the critical threshold parameter is below unity. Finally, some simulations are employed to support the main results and one future research direction is presented.

Lagrangians With Linear Velocities Within Hilfer Fractional Derivative

2011 ◽  
Author(s):  
Dumitru Baleanu ◽  
Om P. Agrawal ◽  
Sami I. Muslih
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Variational Principles ◽  
Major Area ◽  
Lagrange Equations ◽  
Hilfer Fractional Derivative ◽  
Caputo Fractional Derivatives ◽  
Generalized Fractional Derivative

Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.

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