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Abstrakty
A fractional differential equation of real order α, containing variable coefficient t β and a non-homogeneous term, is solved. The general solution is obtained as a sum of Meijer G-functions series determining the solution of a homogeneous counterpart of the considered equation and a series representing the particular solution of a non-homogeneous equation. The convergence of the respective series is analyzed in detail using theorems on properties of Meijer G functions. As an example, two equations, with β = 0 and β = α /2 are studied.
Rocznik
Tom
Strony
71--85
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
autor
- Institute of Mathematics, Czestochowa University of Technology, Poland, klimek@imi.pcz.pl
Bibliografia
- [1] Hilfer R. (Ed.), Applications of Fractional Calclus in Physics, World Scientific, Singapore 2000.
- [2] Magin R.L., Fractional Calculus in Bioengineering, Begell House Publisher, Redding 2006.
- [3] West B.J., Bologna M., Grigolini P., Physics of Fractional Operators, Springer-Verlag, Berlin 2003.
- [4] Agrawal O.P., Tenreiro-Machado J.A., Sabatier J. (Eds.), Fractional Derivatives and their Application: Nonlinear Dynamics, 38, Springer-Verlag, Berlin 2004.
- [5] Metzler R., Klafter J., J. Phys. A 2004, 37, R161.
- [6] Herrmann R., J. Phys. G: Nuc. Phys. 2007, 34, 607.
- [7] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.
- [8] Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley and Sons, New York 1993.
- [9] Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
- [10] Klimek M., Dziembowski D., Mellin Transform for Fractional Differential Equations with Variable Potential, [In:] Nonlinear Science and Complexity, Eds: J.A. Tenreiro-Machado, M.F. Silva, R. Barbosa, Springer-Verlag, Berlin 2009.
- [11] Klimek M., On Solutions of Linear Fractional Differential Equations of a Variational Type, Czestochowa University of Technology Press, Czestochowa 2009 (In press).
- [12] Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives, Gordon & Breach, Amsterdam 1993.
- [13] Kilbas A.A., Saigo M., H-Transforms, Theory and Applications, Chapman & Hall/CRC, Boca Raton 2004.
- [14] Klimek M., Dziembowski D., Sci. Res. Inst. Math. Comp. Science 2008, 7, 31.
- [15] Klimek M., On analogues of exponential functions for antisymmetric fractional derivatives. Computers and Mathematics with Applications, doi:10.1016/j.camwa.2009.08.013, 2009.
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Bibliografia
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bwmeta1.element.baztech-article-BPC6-0004-0034