Mean fractional-order-derivatives differential equations and filters
作者： Michele Caputo
DOI: 10.1007/BF02826009
关键词: Mathematics 、 Numerical partial differential equations 、 Laplace transform applied to differential equations 、 Integro-differential equation 、 Differential equation 、 Reduction of order 、 Examples of differential equations 、 Mathematical analysis 、 Order of accuracy 、 Fractional calculus
摘要: The solution of differential equations fractional order is generalized to the case when derivatives are integrated with respect differentiation. formal found by means Laplace Transform. solutions integro-differential equations, defined and their integrals differentiation, also discussed in terms filtering.
springer.com
sci-hub.se 参考文章(10)
Michele Caputo, The rheology of an anelastic medium studied by means of the observation of the splitting of its eigenfrequencies Journal of the Acoustical Society of America. ,vol. 86, pp. 1984- 1987 ,(1989) , 10.1121/1.398577
Michele Caputo, The Riemann Sheets Solutions of Anelasticity( Annali di Matematica Pura ed Applicata. ,vol. 166, pp. 335- 342 ,(1994) , 10.1007/BF01765641
Kenneth S. Cole, Robert H. Cole, Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics Journal of Chemical Physics. ,vol. 9, pp. 341- 351 ,(1941) , 10.1063/1.1750906
M. Caputo, F. Mainardi, Linear models of dissipation in anelastic solids La Rivista del Nuovo Cimento (1971-1977). ,vol. 1, pp. 161- 198 ,(1971) , 10.1007/BF02820620
R. L. Bagley, P. J. Torvik, A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity Journal of Rheology. ,vol. 27, pp. 201- 210 ,(1983) , 10.1122/1.549724
R. L. Bagley, P. J. Torvik, On the Fractional Calculus Model of Viscoelastic Behavior Journal of Rheology. ,vol. 30, pp. 133- 155 ,(1986) , 10.1122/1.549887
Umberto Cisotti, La Ereditarietà Lineare e i Fenomeni Dispersivi Il Nuovo Cimento. ,vol. 2, pp. 234- 244 ,(1911) , 10.1007/BF02958498
Jean Jacquelin, A number of models for CPA impedances of conductors and for relaxation in non-Debye dielectrics Journal of Non-crystalline Solids. pp. 1080- 1083 ,(1991) , 10.1016/0022-3093(91)90728-O
M. Caputo, Relaxation and free modes of a self-gravitating planet Geophysical Journal International. ,vol. 77, pp. 789- 808 ,(1984) , 10.1111/J.1365-246X.1984.TB02222.X
M. Körnig, G. Müller, Rheological models and interpretation of postglacial uplift Geophysical Journal International. ,vol. 98, pp. 243- 253 ,(1989) , 10.1111/J.1365-246X.1989.TB03349.X