Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution

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Fractional Complex Transform for Fractional Differential Equations (2010, methodology): “In order to illustrate the basic idea of the suggested method, we consider first the following fractional differential equation [5]: ( , ) ( , ), t R , x R, t x u x t k u x t α β + ∂ = ∂ ∈ ∈ (1) which subject to the initial condition”
A Fractional Model of Continuum Mechanics (2012, methodology): “In the onedimensional case, for a particular choice of the region of influence H (4.4) reduces to the modified Riemann-Liouville derivative introduced by Jumarie in [ 26 , 27].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[72] G.”
Application of the Fractional Complex Transform to Fractional Differential Equations (2011, unknown): “[11-13]:”
A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “Definition 6 To overcome the shortcomings, Jumarie [59–62] suggested the following modification of Riemann-Liouville fractional derivative D x (f (x)) = 1 (n− α) d dxn ∫ x”