Solutions with Wright functions for time fractional convection flow near a heated vertical plate
TLDR
In this article, the initial-boundary values problem is determined by means of the Laplace transform technique and are represented by the Wright functions, and a numerical case is analyzed in order to obtain information regarding the influence of the fractional parameters on the temperature and velocity fields.Abstract:
We investigate the unsteady flow of a viscous fluid near a vertical heated plate. The momentum and energy equations are considered as fractional differential equations with respect to the time t. Solutions of the initial-boundary values problem are determined by means of the Laplace transform technique and are represented by means of the Wright functions. The fundamental solution for the temperature field is obtained. This allows obtaining the temperature field for different conditions on the wall temperature. A numerical case is analyzed in order to obtain information regarding the influence of the fractional parameters on the temperature and velocity fields. Some physical aspects of the fluid behavior are presented by graphical illustrations.read more
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Unsteady flow of generalized Casson fluid with fractional derivative due to an infinite plate
TL;DR: In this article, the Caputo time-fractional derivative is introduced in the constitutive model of a generalized Casson fluid which is moving over an infinite, oscillating flat plate, and exact solutions for the fluid velocity and shear stress are obtained using the Laplace transform method.
Journal ArticleDOI
Solutions with special functions for time fractional free convection flow of Brinkman-type fluid
Abstract: The objective of this paper is to report the combined effect of heat and mass diffusion on time fractional free convectional incompressible flow of Brinkman-type fluid over an oscillating plate in the presence of first-order chemical reaction. The Laplace transform has been used to obtain the exact solutions for the fractional-order distributions. Exact expressions for temperature, concentration and velocity have been presented in terms of special functions. For instance, we presented temperature in terms of Wright function, concentration in the form of Fox-H function and velocity in terms of Mittag-Leffler and general Wright functions. The effects of various physical parameters on the fluid motion are sketched and discussed graphically. The present solutions have been reduced by taking one or more parameters approaching to zero and an excellent agreement is observed with the published work. The numerical results for skin-friction, Nusselt and Sherwood numbers have been shown in tabular form.
Journal ArticleDOI
Functionality of circuit via modern fractional differentiations
TL;DR: In this article, the effects of modern fractional differentiation on the RLC electrical circuit via exact analytical approach has been investigated by invoking mathematical Laplace transforms and presented in terms of convolutions product and special function namely Fox-H function.
Journal ArticleDOI
Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium
TL;DR: In this article, a fractional approach namely Caputo-fabrizio fractional operator is applied for developing the governing partial differential equations of Brinkman fluid flow, and the solutions are obtained by integral transforms and presented in special and elementary functions.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
BookDOI
Integral transforms and their applications
Lokenath Debnath,Dambaru Bhatta +1 more
TL;DR: In this article, the authors describe the application of the Fourier Transform in the context of fractional calculus and apply it to the problem of finite differential equations in the complex plane.