Analysis of Fractional Schrödinger Equation Occurring in Quantum Mechanics

Authors

  • V. Parthiban School of Advanced Sciences, VIT University - Chennai Campus, Chennai
  • A. Manivannan School of Advanced Sciences, VIT University - Chennai Campus, Chennai

DOI:

https://doi.org/10.26713/jims.v9i3.763

Keywords:

Fractioanl Schrödinger equaton, Modified Adomian decomposition method, Fractional partial differential equations

Abstract

In this paper, we present Adomian decomposition method to solve linear fuzzy fractional integro-differential equation with fuzzy initial conditions. Results are compared with the results obtained using Fuzzy Laplace transform method.

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References

G. Adomian, Solution of coupled nonlinear partial differential equations by decomposition, Computers and Mathematics with Applicatons 31 (1996), 117–120.

G. Adomian, Solving Frontier Problems of Physics, Kluwer, Netherlands (1994).

J. Biazar, E. Babolian and R. Islam, Solution of the system of ordinary differential equations by Adomian decomposition method, Applied Mathematics and Computation 147 (2004), 713–719.

B. Bonilla, M. Rivero, L. Rodrí­guez Germaá and J.J. Trujillo, Fractional differential equations as alternative models to nonlinear equations, Applied Mathematics and Computation 187 (2007), 79–88.

L. Bougoffa and S. Bougouffa, Adomian method for solving some coupled systems of two equations, Applied Mathematics and Computation 177 (2006), 553–560.

R. Caponetto, G. Dongola, L. Fortuna and I. Petrás, Fractional Order Systems: Modeling and Control Applications, World Scientific Publishing Company, Singapore (2010).

V. Daftardar-Gejji and H. Jafari, Adomian decomposition: a tool for solving a system of fractional differential equations, Journal of Mathematical Analysis and Applications 301 (2005), 508–518.

K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin (2010).

H. Gu and Z. Li, A modified Adomian method for system of nonlinear differential equations, Applied Mathematics and Computation 187 (2007), 748–755.

E. Hernández, D. O'Regan and K. Balachandran, On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear Analysis: Theory, Methods and Applications 73 (2010), 3462–3471.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).

N. Laskin, Fractals and quantum mechanics, Chaos 10 (2000), 780–790.

N. Laskin, Fractional Schrödiner equation, Physics Review E 66 (5) (2002), 056108, doi:10.1103/PhysRevE.66.056108.

J.T. Machado, V. Kiryakova and F. Mainardi, Recent history of fractional calculus, Communication in Nonlinear Science and Numerical Simulation 16 (2010), 1140–1153.

F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, Singapore (2010).

K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley and Sons, New York (1993).

K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, San Diego (1974).

V. Parthiban and K. Balachandran, Solutions of system of fractional partial differential equaions, Applications and Applied Mathematics, An International Journal 8 (1) (June 2013), 289 – 304.

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

A.S.V. Ravi Kanth and K. Aruna, Two dimensional differential transform method for solving linear and nonlinear Schrödinger equation, Chaos, Solitons & Fractals 41 (2009), 2277–2281.

S.Z. Rida, H.M. El-Sherbiny and A.A.M. Arafa, On the solution of the fractional nonlinear Schrödinger equation, Physics Letters A 372 (2008) 553-558.

A. Sadighi and D.D. Ganji, Analytic treatment of linear and nonlinear Schrödinger equations: A study with homotopy-perturbation and Adomian decomposition methods, Physics Letters A 372 (2008), 465–469.

S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Gordan and Breach, Amsterdam (1993).

R.K. Saxena, R. Saxena and S.L. Kalla, Computational solution of a fractional generalization of the Schrödiner equation occurring in quantum mechanics, Applied Mathematics and Computation 216 (2010), 1412-1417.

E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Phys. Rev. 28 (6) (1926), 1049–1070.

H. Wang, Numerical studies on the split-step finite difference method for nonlinear Schrödiner equations, Applied Mathematics and Computation 170 (2005), 17–35.

A.M. Wazwaz, A study of linear and nonlinear Schrödiner equation by the variational iteration method, Chaos Solitons & Fractals 37 (2008), 1136–1142.

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How to Cite

Parthiban, V., & Manivannan, A. (2017). Analysis of Fractional Schrödinger Equation Occurring in Quantum Mechanics. Journal of Informatics and Mathematical Sciences, 9(3), 595–607. https://doi.org/10.26713/jims.v9i3.763

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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