Analytical Solution of the Space-Time Fractional Nonlinear Schrödinger Equation

• Published in: Reports on mathematical physics Vol. 77; no. 1; pp. 19 - 34
• Main Authors: Abdel-Salam, Emad A-B., Yousif, Eltayeb A., El-Aasser, Mostafa A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2016
• Subjects: Differential equations; fractional Riccati expansion method; Hyperbolic functions; Mathematical analysis; modified Riemann–Liouville derivatives; nonlinear fractional differential equation; Nonlinearity; Schroedinger equation; space-time fractional nonlinear Schrödinger equation; modified Riemann–Liouville derivatives; space-time fractional nonlinear Schrödinger equation; nonlinear fractional differential equation; fractional Riccati expansion method
• ISSN: 0034-4877; 1879-0674
• DOI: 10.1016/S0034-4877(16)30002-7

The space-time fractional nonlinear Schrödinger equation is solved by mean of on the fractional Riccati expansion method. These solutions include generalized trigonometric and hyperbolic functions which could be useful for further understanding of mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.