Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations

Z. Navickas, T. Telksnys, R. Marcinkevicius and M. Ragulskis

Chaos, Solitons & Fractals, 2017, vol. 104, issue C, 625-634

Abstract: An operator-based framework for the construction of analytical soliton solutions to fractional differential equations is presented in this paper. Fractional differential equations are mapped from Caputo algebra to Riemann-Liouville algebra in order to preserve the additivity of base function powers under multiplication. The proposed technique is used for the construction of solutions to a class of fractional Riccati equations. Recurrence relations between power series parameters yield generating functions which are used to construct explicit expressions of closed-form solutions.

Keywords: Fractional differential equation; Operator calculus; Analytical solution; Closed-form solution; Soliton solution (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:104:y:2017:i:c:p:625-634

DOI: 10.1016/j.chaos.2017.09.026

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