Homotopy Analysis Method for Time-Fractional Schrödinger Equations

Nauman ASGHAR; Kamran ALI; Ahmet YILDIRIM; Syed Tauseef MOHYUD-DIN

Authors

Nauman ASGHAR Department of Mathematics, HITEC University, Taxila Cantt
Kamran ALI Department of Mathematics, HITEC University, Taxila Cantt
Ahmet YILDIRIM Ege University, Department of Mathematics, 35100 Bornova-İzmir
Syed Tauseef MOHYUD-DIN Department of Mathematics, HITEC University, Taxila Cantt

Keywords:

Homotopy Analysis Method, fractional Schrödinger partial differential equations, nonlinear problems

Abstract

The Homotopy Analysis Method (HAM) is applied to tackle time-fractional Schrödinger equations. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Author Biography

Syed Tauseef MOHYUD-DIN, Department of Mathematics, HITEC University, Taxila Cantt

Department of Mathematics, HITEC University

References

S Abbasbandy. Homotopy analysis method for generalized Benjamin-Bona-Mahony equation. Z. Angew. Math. Phys. 2008; 59, 51-62.

S Abbasbandy and FS Zakaria. Soliton solutions for the fifth-order K-dV equation with the homotopy analysis method. Nonlinear Dyn. 2008; 51, 83-7.

S Abbasbandy. Homotopy analysis method for the Kawahara equation. Nonlinear Anal. B 2010; 11, 307-12.

S Abbasbandy, E Shivanian and K Vajravelu. Mathematical properties of curve in the framework of the homotopy analysis method. Comm. Non. Sci. Numer. Simulat. 2011; 16, 4268-75.

S Abbasbandy. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 2006; 360, 109-13.

S Abbasbandy. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys. Lett. A 2007; 361, 478-83.

SJ Liao. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton, Chapman and Hall, 2003.

SJ Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004; 147, 499-513.

SJ Liao. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 2005; 169, 1186-94.

ME Gurtin and RC Maccamy. On the diffusion of biological population. Math. Biosci. 1977; 33, 35-49.

WSC Gurney and RM Nisbet. The regulation of in homogenous populations. J. Theor. Biol. 1975; 52, 441-57.

YG Lu. Holder estimates of solution of biological population equations. Appl. Math. Lett. 2000; 13, 123-6.

Y Tan and S Abbasbandy. Homotopy analysis method for quadratic Riccati differential equation. Commun. Nonlin. Sci. Numer. Simul. 2008; 13, 539-46.

T Hayat, M Khan and S Asghar. Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta. Mech. 2004; 168, 213-32.

T Hayat and M Khan. Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dyn. 2005; 42, 395-405.

ST Mohyud-Din and A Yildirim. The numerical solution of three dimensional Helmholtz equations. Chinese Phys. Lett. 2010; 27, 060201.

A Yildirim and ST Mohyud-Din. Analytical approach to space and time fractional Burger’s equations. Chinese Phys. Lett. 2010; 27, 090501.

I Podlubny. Fractional Differential Equations. Academic Press, New York, 1999.

L Song and H Zhang. Application of Homotopy analysis method to fractional Kdv-Burgers- Kuramoto equation. Phys. Lett. A 2007; 367, 88-94.

M Ganjiani. Solution of nonlinear fractional differential equation using homotopy analysis method. Appl. Math. Model. 2010; 34, 1634-41.

H Jafari and S Seifi. Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. Comun. Nonlin. Sci. Num. Sim. 2009; 14, 2006-12.