Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology

• Published in: Chinese journal of physics (Taipei) Vol. 56; no. 1; pp. 75 - 85
• Main Authors: Kumar, Dipankar, Seadawy, Aly R., Joardar, Atish Kumar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2018
• Subjects: Conformable derivative; Exact solutions; Fractional biological population model; Fractional diffusion-reaction equation; Fractional generalized reaction duffing equations; Modified Kudryashov method; Symbolic computation; Fractional generalized reaction duffing equations; Exact solutions; Fractional biological population model; Fractional diffusion-reaction equation; Modified Kudryashov method; Conformable derivative; Symbolic computation
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2017.11.020

•The hydrodynamic biological mathematical models were given.•Fractional biological population model was discussed.•We presented fractional generalized diffusion-reaction equations.•New exact travelling wave solutions were obtained. In this study, the modified Kudryashov method is used to construct new exact solutions for some conformable fractional differential equations. By implementing the conformable fractional derivative and compatible fractional complex transforms, the fractional generalized reaction duffing (RD) model equation, the fractional biological population model and the fractional diffusion reaction (DR) equation with quadratic and cubic nonlinearity are discussed. As an outcome, some new exact solutions are formally established. All solutions have been verified back into its corresponding equation with the aid of maple package program. We assure that the employed method is simple and robust for the estimation of the new exact solutions, and practically capable for reducing the size of computational work for solving a various class of fractional differential equations arising in applied mathematics, mathematical physics and biology.