Fractional Complex Transform for Fractional Differential Equations

By Zheng-Biao Li, Ji-Huan He. 2010

334 citations recorded by the source corpus.

Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a7422ecbb62e48f7f3839077393c2b89257678a1

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, methodology): “Some useful formulas and results of the fractional modified Riemann–Liouville derivative are summarized in References [24, 25].”
A note on exp-function method combined with complex transform method applied to fractional differential equations (2015, methodology): “The fractional complex transform [25, 33, 34] is the simplest approach to convert fractional di erential equations into ordinary di erential equations.”
Application of the Fractional Complex Transform to Fractional Differential Equations (2011, positive): “Very recently the fractional complex transform [7-10] was suggested to convert fractional order differential equations with modified Riemann-Liouville derivatives [11-13] into integer order differential equations, and the resultant equations can be solved by advanced calculus.”
Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations (2013, background): “Li and He [25, 26] suggested a fractional complex transform to convert fractional differential equations into ordinary differential equations, so all analytical methods devoted to the advanced calculus can be easily applied to the fractional calculus.”
A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, positive): “The fractional complex transform was first proposed in 2010 [94] to convert fractional differential equations into ordinary differential equations.”
An Extended Fractional Complex Transform (2010, background): “[1], it can convert some kinds of fractional differential equations into ordinary differential equations.”
Advanced Local Fractional Calculus and Its Applications (2012, neutral): “[75] Z.”