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

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.