Solutions with Wright Function for Time Fractional Free Convection Flow of Casson Fluid

A fractional model of Casson fluid coupled with energy equation is developed. Casson fluid in the presence of heat transfer is considered over an oscillating vertical plate with constant wall temperature. Definition of fractional Caputo derivative is used in the mathematical formulation of the problem. Exact solutions via Laplace transform are obtained and presented in terms of Wright function. Parametric studies were undertaken, and the obtained solutions are illustrated through plots for various physical parameters.

[1]  M. El-shahed,et al.  An Extension of Wright Function and Its Properties , 2015 .

[2]  Babak Parvin,et al.  Temporal behavior of an atom-cavity system in two distinct regimes , 2016 .

[3]  Hossein Jafari,et al.  Solving a multi-order fractional differential equation using adomian decomposition , 2007, Appl. Math. Comput..

[4]  E. M. Wright,et al.  On the Coefficients of Power Series having Exponential Singularities (Second Paper) , 1949 .

[5]  E. Wright.  THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE , 1940 .

[6]  Ranjan K. Dash,et al.  Casson fluid flow in a pipe filled with a homogeneous porous medium , 1996 .

[7]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[8]  S. Pramanik,et al.  Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation , 2014 .

[9]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[10]  I. Petráš.  Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[11]  R. Bagley,et al.  A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity , 1983 .

[12]  K. S. Chaudhuri,et al.  Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method , 2006, Appl. Math. Comput..

[13]  Ilyas Khan,et al.  Unsteady mhd free convection flow of casson fluid past over an oscillating vertical plate embedded in a porous medium , 2015 .

[14]  Shaher Momani,et al.  Decomposition method for solving fractional Riccati differential equations , 2006, Appl. Math. Comput..

[15]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[16]  Shaher Momani,et al.  Homotopy perturbation method for nonlinear partial differential equations of fractional order , 2007 .

[17]  E. Wright.  On the Coefficients of Power Series Having Exponential Singularities , 1933 .

[18]  Muhammad Aslam Noor,et al.  Numerical methods for fourth-order fractional integro-differential equations , 2006, Appl. Math. Comput..

[19]  M. E. Bise,et al.  Fractional calculus application in control systems , 1990, IEEE Conference on Aerospace and Electronics.

[20]  N. Sweilam,et al.  Numerical studies for a multi-order fractional differential equation , 2007 .

[21]  Fawang Liu,et al.  Numerical solution of the space fractional Fokker-Planck equation , 2004 .

[22]  Santos B. Yuste,et al.  Weighted average finite difference methods for fractional diffusion equations , 2004, J. Comput. Phys..

[23]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[24]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[25]  Tan Wen-chang,et al.  A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates , 2003 .

[26]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[27]  Ilyas Khan,et al.  Unsteady flow of generalized Casson fluid with fractional derivative due to an infinite plate , 2016 .

[28]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[29]  S. Momani,et al.  Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order , 2008 .

[30]  S. Momani,et al.  Analytical approach to linear fractional partial differential equations arising in fluid mechanics , 2006 .

[31]  Qi Wang,et al.  Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method , 2006, Appl. Math. Comput..

[32]  Haitao Qi,et al.  Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial Cylinders , 2006 .

[33]  Mohsen Fathi,et al.  Gravitational collapse in repulsive $R+\mu^{4}/R$R+μ4/R gravity , 2016 .

[34]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[35]  N. Casson,et al.  A flow equation for pigment-oil suspensions of the printing ink type , 1959 .

[36]  M. Shitikova,et al.  Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids , 1997 .

[37]  Constantin Fetecau,et al.  Effects of the fractional order and magnetic field on the blood flow in cylindrical domains , 2016 .