OPERATIONAL METHOD FOR THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES

作者: Rudolf Hilfer , Zivorad Tomovski , Yury Luchko

DOI:

关键词:

摘要: The operational calculus is an algorithmic approach for the solution of initial-value problems difierential, integral, and integro-difierential equations. In this paper, Mikusinski type a generalized Riemann-Liouville fractional difierential operator with types introduced by one authors developed. traditional Riemann- Liouville Liouville-Caputo derivatives correspond to particu- lar general one-parameter family same order. constructed in paper used solve corresponding initial value problem n-term lin- ear equation these arbitrary orders constant coe-cients. Special cases obtained solutions are presented.

参考文章(27)
Tilak Raj Prabhakar, A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学. ,vol. 19, pp. 7- 15 ,(1971)
M. Caputo, Linear models of dissipation whose Q is almost frequency independent Annals of Geophysics. ,vol. 19, pp. 383- 393 ,(1966) , 10.4401/AG-5051
Francesco Mainardi, Rudolf Gorenflo, Fractional Calculus: Integral and Differential Equations of Fractional Order arXiv: Mathematical Physics. ,(2008)
Oleg Igorevich Marichev, Stefan G Samko, Anatoly A Kilbas, Fractional Integrals and Derivatives: Theory and Applications ,(1993)
Yurii F. Luchko, Semen B. Yakubovich, The Hypergeometric Approach to Integral Transforms and Convolutions ,(1994)
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)