-
1
-
-
84941480860
-
Some existence theorems on differential equations of generalized order
-
M. A. Al-Bassam, Some existence theorems on differential equations of generalized order, J. Reine Angew. Math., 218 (1965), pp. 70-78.
-
(1965)
J. Reine Angew. Math
, vol.218
, pp. 70-78
-
-
Al-Bassam, M.A.1
-
3
-
-
79953685491
-
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
-
E. Capelas de Oliveira, F. Mainardi, and J. Vaz, Jr., Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics, Eur. Phys. J. Special Topics, 193 (2011), pp. 161-171.
-
(2011)
Eur. Phys. J. Special Topics
, vol.193
, pp. 161-171
-
-
Oliveira De E.Capelas1
Mainardi, F.2
Vaz, J.3
-
4
-
-
51649182765
-
Linear models of dissipation in anelastic solids
-
M. Caputo and F. Mainardi, Linear models of dissipation in anelastic solids, Riv. Nuovo Cimento (Ser. II), 1 (1971), pp. 161-198.
-
(1971)
Riv. Nuovo Cimento (Ser. II)
, vol.1
, pp. 161-198
-
-
Caputo, M.1
Mainardi, F.2
-
5
-
-
84869187898
-
A new dissipation model based on memory mechanism
-
M. Caputo and F. Mainardi, A new dissipation model based on memory mechanism, Fract. Calc. Appl. Anal., 10 (2007), pp. 309-324;
-
(2007)
Fract. Calc. Appl. Anal
, vol.10
, pp. 309-324
-
-
Caputo, M.1
Mainardi, F.2
-
6
-
-
84937842200
-
-
reprinted from
-
reprinted from Pure Appl. Geophys., 9 (1971), pp. 134-147.
-
(1971)
Pure Appl. Geophys
, vol.9
, pp. 134-147
-
-
-
7
-
-
0004158133
-
-
2nd ed., Comput. Sci. Appl. Math., Academic Press Inc., Orlando, FL
-
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Comput. Sci. Appl. Math., Academic Press Inc., Orlando, FL, 1984.
-
(1984)
Methods of Numerical Integration
-
-
Davis, P.J.1
Rabinowitz, P.2
-
8
-
-
84929302772
-
An improved Talbot method for numerical Laplace transform inversion
-
B. Dingfelder and J. A. C. Weideman, An improved Talbot method for numerical Laplace transform inversion, Numer. Algorithms, 68 (2015), pp. 167-183.
-
(2015)
Numer. Algorithms
, vol.68
, pp. 167-183
-
-
Dingfelder, B.1
Weideman, J.A.C.2
-
9
-
-
0003031851
-
Fractional derivatives and the Cauchy problem for differential equations of fractional order
-
M. M. Džrbašjan and A. B. Nersesjan, Fractional derivatives and the Cauchy problem for differential equations of fractional order, Izv. Akad. Nauk Armjan. SSR Ser. Mat., 3 (1968), pp. 3-29.
-
(1968)
Izv. Akad. Nauk Armjan. SSR Ser. Mat
, vol.3
, pp. 3-29
-
-
Džrbašjan, M.M.1
Nersesjan, A.B.2
-
10
-
-
0007268717
-
The asymptotic expansion of integral functions defined by generalized hypergeometric functionss
-
C. Fox, The asymptotic expansion of integral functions defined by generalized hypergeometric functionss, Proc. London Math. Soc., 27 (1928), pp. 389-400.
-
(1928)
Proc. London Math. Soc
, vol.27
, pp. 389-400
-
-
Fox, C.1
-
12
-
-
84937863090
-
Solving the time-fractional Schrödinger equation by Krylov projection methods
-
R. Garrappa, I. Moret, and M. Popolizio, Solving the time-fractional Schrödinger equation by Krylov projection methods, J. Comput. Phys., 293 (2015), pp. 115-134.
-
(2015)
J. Comput. Phys
, vol.293
, pp. 115-134
-
-
Garrappa, R.1
Moret, I.2
Popolizio, M.3
-
13
-
-
79961015107
-
Generalized exponential time differencing methods for fractional order problems
-
R. Garrappa and M. Popolizio, Generalized exponential time differencing methods for fractional order problems, Comput. Math. Appl., 62 (2011), pp. 876-890.
-
(2011)
Comput. Math. Appl
, vol.62
, pp. 876-890
-
-
Garrappa, R.1
Popolizio, M.2
-
14
-
-
84879234882
-
Evaluation of generalized Mittag-Leffler functions on the real line
-
R. Garrappa and M. Popolizio, Evaluation of generalized Mittag-Leffler functions on the real line, Adv. Comput. Math., 39 (2013), pp. 205-225.
-
(2013)
Adv. Comput. Math
, vol.39
, pp. 205-225
-
-
Garrappa, R.1
Popolizio, M.2
-
15
-
-
33749034221
-
Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces
-
I. P. Gavrilyuk and V. L. Makarov, Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces, SIAM J. Numer. Anal., 43 (2005), pp. 2144-2171.
-
(2005)
SIAM J. Numer. Anal
, vol.43
, pp. 2144-2171
-
-
Gavrilyuk, I.P.1
Makarov, V.L.2
-
16
-
-
84922721300
-
-
Springer Monogr. Math., Springer, Heidelberg
-
R. Gorenflo, A. A. Kilbas, F. Mainardi, and S. V. Rogosin, Mittag-Leffler functions, Related Topics and Applications, Springer Monogr. Math., Springer, Heidelberg, 2014.
-
(2014)
Mittag-Leffler Functions Related Topics and Applications
-
-
Gorenflo, R.1
Kilbas, A.A.2
Mainardi, F.3
Rogosin, S.V.4
-
17
-
-
2942584456
-
Computation of the Mittag-Leffler function Eα, β(z) and its derivative
-
R. Gorenflo, J. Loutchko, and Y. Luchko, Computation of the Mittag-Leffler function Eα, β(z) and its derivative, Fract. Calc. Appl. Anal., 5 (2002), pp. 491-518.
-
(2002)
Fract. Calc. Appl. Anal
, vol.5
, pp. 491-518
-
-
Gorenflo, R.1
Loutchko, J.2
Luchko, Y.3
-
19
-
-
33746792356
-
Computation of the generalized Mittag-Leffler function and its inverse in the complex plane
-
R. Hilfer and H. J. Seybold, Computation of the generalized Mittag-Leffler function and its inverse in the complex plane, Integral Transforms Spec. Funct., 17 (2006), pp. 637-652.
-
(2006)
Integral Transforms Spec. Funct
, vol.17
, pp. 637-652
-
-
Hilfer, R.1
Seybold, H.J.2
-
20
-
-
0001233578
-
On the theory of linear integral equations
-
E. Hille and J. D. Tamarkin, On the theory of linear integral equations, Ann. of Math. (2), 31 (1930), pp. 479-528.
-
(1930)
Ann. of Math
, vol.31
, Issue.2
, pp. 479-528
-
-
Hille, E.1
Tamarkin, J.D.2
-
21
-
-
77956684069
-
Theory and applications of fractional differential equations
-
Elsevier Science B.V., Amsterdam
-
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science B.V., Amsterdam, 2006.
-
(2006)
North-Holland Math. Stud
, vol.204
-
-
Kilbas, A.A.1
Srivastava, H.M.2
Trujillo, J.J.3
-
22
-
-
33749020865
-
A spectral order method for inverting sectorial Laplace transforms
-
M. López-Fernández, C. Palencia, and A. Schädle, A spectral order method for inverting sectorial Laplace transforms, SIAM J. Numer. Anal., 44 (2006), pp. 1332-1350.
-
(2006)
SIAM J. Numer. Anal
, vol.44
, pp. 1332-1350
-
-
López-Fernández, M.1
Palencia, C.2
Schädle, A.3
-
24
-
-
0000145521
-
On Mittag-Leffler-type functions in fractional evolution processes
-
F. Mainardi and R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes, J. Comput. Appl. Math., 118 (2000), pp. 283-299.
-
(2000)
J. Comput. Appl. Math
, vol.118
, pp. 283-299
-
-
Mainardi, F.1
Gorenflo, R.2
-
27
-
-
84876259043
-
A note on Krylov methods for fractional evolution problems
-
I. Moret, A note on Krylov methods for fractional evolution problems, Numer. Funct. Anal. Optim., 34 (2013), pp. 539-556.
-
(2013)
Numer. Funct. Anal. Optim
, vol.34
, pp. 539-556
-
-
Moret, I.1
-
28
-
-
81555222614
-
On the convergence of Krylov subspace methods for matrix Mittag-Leffler functions
-
I. Moret and P. Novati, On the convergence of Krylov subspace methods for matrix Mittag-Leffler functions, SIAM J. Numer. Anal., 49 (2011), pp. 2144-2164.
-
(2011)
SIAM J. Numer. Anal
, vol.49
, pp. 2144-2164
-
-
Moret, I.1
Novati, P.2
-
29
-
-
0025448483
-
Algorithm 682: Talbot's method of the Laplace inversion problems
-
A. Murli and M. Rizzardi, Algorithm 682: Talbot's method of the Laplace inversion problems, ACM Trans. Math. Software, 16 (1990), pp. 158-168.
-
(1990)
ACM Trans. Math. Software
, vol.16
, pp. 158-168
-
-
Murli, A.1
Rizzardi, M.2
-
30
-
-
10644284401
-
Fractional differential equations, an introduction to fractional derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications
-
Academic Press Inc., San Diego, CA
-
I. Podlubny, Fractional Differential Equations, An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Math. Sci. Engrg. 198, Academic Press Inc., San Diego, CA, 1999.
-
(1999)
Math. Sci. Engrg
, vol.198
-
-
Podlubny, I.1
-
32
-
-
0842337110
-
A singular integral equation with a generalized Mittag-Leffler function in the kernel
-
T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), pp. 7-15.
-
(1971)
Yokohama Math. J
, vol.19
, pp. 7-15
-
-
Prabhakar, T.R.1
-
33
-
-
55349106156
-
Numerical algorithm for calculating the generalized Mittag-Leffler function
-
H. Seybold and R. Hilfer, Numerical algorithm for calculating the generalized Mittag-Leffler function, SIAM J. Numer. Anal., 47 (2008), pp. 69-88.
-
(2008)
SIAM J. Numer. Anal
, vol.47
, pp. 69-88
-
-
Seybold, H.1
Hilfer, R.2
-
34
-
-
0345016412
-
A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
-
D. Sheen, I. H. Sloan, and V. Thomée, A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature, IMA J. Numer. Anal., 23 (2003), pp. 269-299.
-
(2003)
IMA J. Numer. Anal
, vol.23
, pp. 269-299
-
-
Sheen, D.1
Sloan, I.H.2
Thomée, V.3
-
35
-
-
0002152334
-
The accurate numerical inversion of Laplace transforms
-
A. Talbot, The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl., 23 (1979), pp. 97-120.
-
(1979)
J. Inst. Math. Appl
, vol.23
, pp. 97-120
-
-
Talbot, A.1
-
36
-
-
84905981043
-
The exponentially convergent trapezoidal rule
-
L. N. Trefethen and J. A. C. Weideman, The exponentially convergent trapezoidal rule, SIAM Rev., 56 (2014), pp. 385-458.
-
(2014)
SIAM Rev
, vol.56
, pp. 385-458
-
-
Trefethen, L.N.1
Weideman, J.A.C.2
-
37
-
-
33749016203
-
Talbot quadratures and rational approximations
-
L. N. Trefethen, J. A. C. Weideman, and T. Schmelzer, Talbot quadratures and rational approximations, BIT, 46 (2006), pp. 653-670.
-
(2006)
BIT
, vol.46
, pp. 653-670
-
-
Trefethen, L.N.1
Weideman, J.A.C.2
Schmelzer, T.3
-
39
-
-
34548172888
-
Optimizing Talbot's contours for the inversion of the Laplace transform
-
J. A. C. Weideman, Optimizing Talbot's contours for the inversion of the Laplace transform, SIAM J. Numer. Anal., 44 (2006), pp. 2342-2362.
-
(2006)
SIAM J. Numer. Anal
, vol.44
, pp. 2342-2362
-
-
Weideman, J.A.C.1
-
40
-
-
76549125164
-
Improved contour integral methods for parabolic PDEs
-
J. A. C. Weideman, Improved contour integral methods for parabolic PDEs, IMA J. Numer. Anal., 30 (2010), pp. 334-350.
-
(2010)
IMA J. Numer. Anal
, vol.30
, pp. 334-350
-
-
Weideman, J.A.C.1
-
41
-
-
34548162562
-
Parabolic and hyperbolic contours for computing the Bromwich integral
-
J. A. C. Weideman and L. N. Trefethen, Parabolic and hyperbolic contours for computing the Bromwich integral, Math. Comp., 76 (2007), pp. 1341-1356.
-
(2007)
Math. Comp
, vol.76
, pp. 1341-1356
-
-
Weideman, J.A.C.1
Trefethen, L.N.2
-
42
-
-
0001799540
-
Über den fundamentalsatz in der teorie der funktionen Eα(x)
-
A. Wiman, Über den fundamentalsatz in der teorie der funktionen Eα(x), Acta Math., 29 (1905), pp. 191-201.
-
(1905)
Acta Math
, vol.29
, pp. 191-201
-
-
Wiman, A.1
-
43
-
-
84937881946
-
-
Wolfram Research Inc
-
Wolfram Research Inc., Tricomi Confluent Hypergeometric Function, 1998-2010, http://functions.wolfram.com/HypergeometricFunctions/HypergeometricU/.
-
(1998)
Tricomi Confluent Hypergeometric Function
-
-
-
44
-
-
84963044459
-
The asymptotic expansion of the generalized hypergeometric function
-
E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc., s-1-10 (1935), pp. 286-293.
-
(1935)
J. London Math. Soc., s-1-10
, pp. 286-293
-
-
Wright, E.M.1
|