Solution of nonlinear space time fractional differential equations via\n the fractional projective Riccati expansion method

2015/04/14 by Emad A.‐B. Abdel‐Salam, Abdel-Salam, Emad A-B., Eltayeb A. Yousif +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Solar and Stellar Astrophysics (astro-ph.SR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1504.03450

openalex publication_date 2015/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the fractional projective Riccati expansion method is proposed\nto solve fractional differential equations. To illustrate the effectiveness of\nthe method, we discuss the space-time fractional Burgers equation, the\nspace-time fractional mKdV equation and time fractional biological population\nmodel. The solutions are expressed in terms of fractional hyperbolic functions.\nThese solutions are useful to understand the mechanisms of the complicated\nnonlinear physical phenomena and fractional differential equations. Among these\nsolutions, some are found for the first time. The fractal index for the\nobtained results is equal to one. Counter examples to compute the fractal index\nare introduced in appendix.\n

Citations

• The Fractal Geometry of Nature
• Fractional Differential Equations

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