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Anomalous diffusion equation using a new general fractional derivative within the Miller–Ross kernel

School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

E-mail Address: yyfeng12cumt@163.com

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Jiangen Liu

State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

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https://doi.org/10.1142/S0217984920502899Cited by:4 (Source: Crossref)

Abstract

In view of the generalization of Miller–Ross kernel in the sense of Riemann–Liouville type, we propose the new definitions of the general fractional integral (GFI) and general fractional derivative (GFD) to discuss the anomalous diffusion equation, which is distinct from those classic calculus operators. The obtained analytical solution of the application described in the graph is effective and accurate making the use of Laplace transform.

Keywords:

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