TY - JOUR

T1 - Exact solutions to a class of time fractional evolution systems with variable coefficients

AU - Dorjgotov, Khongorzul

AU - Ochiai, Hiroyuki

AU - Zunderiya, Uuganbayar

N1 - Funding Information:
We are very grateful to an anonymous referee whose valuable suggestions and comments helped us to improve the content of the manuscript. This work was supported by JSPS. (KAKENHI Grant No. 15H03613) and by the National University of Mongolia (Grant No. P2017-2475).

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We explicitly give new group invariant solutions to a class of Riemann-Liouville time fractional evolution systems with variable coefficients. These solutions are derived from every element in an optimal system of Lie algebras generated by infinitesimal symmetries of evolution systems in the class. We express the solutions in terms of Mittag-Leffler functions, generalized Wright functions, and Fox H-functions and show that these solutions solve diffusion-wave equations with variable coefficients. These solutions contain previously known solutions as particular cases. Some plots of solutions subject to the order of the fractional derivative are illustrated.

AB - We explicitly give new group invariant solutions to a class of Riemann-Liouville time fractional evolution systems with variable coefficients. These solutions are derived from every element in an optimal system of Lie algebras generated by infinitesimal symmetries of evolution systems in the class. We express the solutions in terms of Mittag-Leffler functions, generalized Wright functions, and Fox H-functions and show that these solutions solve diffusion-wave equations with variable coefficients. These solutions contain previously known solutions as particular cases. Some plots of solutions subject to the order of the fractional derivative are illustrated.

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U2 - 10.1063/1.5035392

DO - 10.1063/1.5035392

M3 - Article

AN - SCOPUS:85051486008

SN - 0022-2488

VL - 59

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

M1 - 081504

ER -