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Published on: November 11, 2013
Fractional calculus with exponential memory
Hui Fu1, Guo-Cheng Wu1, Guang Yang1
1Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, People's Republic of China.
Abstract:
The standard definition of the Riemann-Liouville integral is revisited. A new fractional integral is proposed with an exponential kernel. Furthermore, some useful properties such as composition relationship of the new fractional integral and Leibniz integral law are provided. Exact solutions of the fractional homogeneous equation and the non-homogeneous equations are given, respectively. Finally, a finite difference scheme is proposed for solving fractional nonlinear differential equations with exponential memory. The results show the efficiency and convenience of the new fractional derivative.
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