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Exact solutions of time-fractional heat conduction equation by the fractional complex transform

Li Zheng-Biao (College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan, China)
Zhu Wei-Hong (Research Center of Educational Science, Qujing Normal University, Qujing, Yunnan, China)
He Ji-Huan (National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, China)

The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.

Keywords: Fractional Complex Transform, Modified Riemann-Liouville derivative, time-fractional Heat Conduction Equation, exact solution