A novel method for nonlinear fractional differential equations using symbolic computation. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Guner, Ozkan; Bekir, Ahmet
• Is Part Of: Waves in random and complex media. Volume 27:Issue 1(2017)
• Page Start: 163
• Page End: 170
• Publication Date: 2017-01-02
• Subjects: 35C08 -- 35Q68 -- 34A08; Electromagnetic waves -- Periodicals; Electromagnetic waves -- Scattering -- Periodicals; 531.1133
• DOI: 10.1080/17455030.2016.1213462
• Languages: English
• ISSNs: 1745-5030

Abstract

Abstract : In this paper, a new approach, namely an ansatz method is applied to find exact solutions for nonlinear fractional differential equations in the sense of modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to solve the fractional-order biological population model and the space–time fractional modified equal width equation, and as a result, some dark soliton solutions for them are established.