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Generalized space–time fractional diffusion equation with composite fractional time derivative
Physica A: Statistical Mechanics and its Applications, 2012Abstract We investigate the solution of space–time fractional diffusion equations with a generalized Riemann–Liouville time fractional derivative and Riesz–Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation.
Tomovski, Zivorad +3 more
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Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative
Journal of Physics A: Mathematical and Theoretical, 2011In this paper, the solution of a fractional diffusion equation with a Hilfer-generalized Riemann–Liouville time fractional derivative is obtained in terms of Mittag–Leffler-type functions and Fox's H-function. The considered equation represents a quite general extension of the classical diffusion (heat conduction) equation. The methods of separation of
Trifce Sandev +2 more
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Fractional derivatives: integral representations and generalized polynomials
2004Summary: We show that the use of functions associated with generalized forms of Hermite polynomials provide a natural tool for the solution of partial differential equations involving fractional derivatives. Within such a context we clarify the meaning of exponential operators with fractional derivatives and discuss alternative definitions based on ...
DATTOLI G +3 more
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Taylor’s Series Generalized for Fractional Derivatives and Applications
SIAM Journal on Mathematical Analysis, 1971The familiar Taylor’s series expansion of the function , $f(z)$ has for its general term $D^n f(z_0 ){{(z - z_0 )^n } / {n!}}$. A new generalization of Taylor’s series in which the general term is $D^{an + \gamma } f(z_0 ){{(z - z_0 )^{an + \gamma } } / {\Gamma (an + \gamma + 1)}}$, where $a > 0$ and $\gamma $ is an arbitrary complex number, is ...
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Fractional Flow Reserve or Intravascular Ultrasonography to Guide PCI
New England Journal of Medicine, 2022Jinlong Zhang, Joo-Yong Hahn, Wenming He
exaly
Operational Calculus for the General Fractional Derivative and Its Applications
Fractional Calculus and Applied Analysis, 2021Yuri Luchko
exaly