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

An Operator-Based Approach for the Construction of Closed-Form Solutions to Fractional Differential Equations

“…An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The considered technique is a generalization of the results presented in [26] for rational-valued fractional derivative order. Caputo and Riemann-Liouville fractional differentiation and integration operators are defined for respective sets of fractional power series.…”

“…A generalization of algebras and operators given in [26] for fractional derivatives of order α = 1 n , n ∈ N is presented in this section.…”

“…to recurrence (3.23). Using the method of undetermined coefficients, an initial guess for q j reads: 26) where ν 0 , ν 1 , ν 2 ∈ C are undetermined constants. It is clear that q j = a j = 0 for j = 3, 4, .…”

“…However, the presented technique is not limited to such equations -it can also be used to construct solutions to linear FDEs with variable coefficients or nonlinear problems. It has already been shown for the special case of fractional derivative order 1 2 in [26] that an approach based on fractional power series can be used to construct solutions to nonlinear fractional differential equations.…”

“…The main objective of this paper is to develop an operator-based approach for the construction of closed-form solutions to fractional differential equations. Some key concepts of such operator-based techniques are presented in [26] for fractional derivative order α = 1 2 . A generalization of this technique for rational-valued fractional derivative order α = m n is presented in this paper.…”