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(24)
Introduction to functional differential equations
Fractional Integrals and Derivatives: Theory and Applications
An Introduction to the Fractional Calculus and Fractional Differential Equations
THEORY OF FRACTIONAL DIFFERENTIAL INEQUALITIES AND APPLICATIONS
Fractional integrals and derivatives
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Fractional differential equations
Fractional differential equations,I. Podlubny
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Fractional differential equations
(
Citations: 1049
)
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I. Podlubny
Published in 1999.
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(71)
...Variety of models having positive linear behavior can be found in engineering, management sciences,economics,socialsciences,biology,medicine,etc.Mathematical fundamentals of the fractional calculus are given in the monographs [25]–[
27
], [29] and the fractional differential equations and their applications have been addressed in [20], [22], and [23]...
Tadeusz Kaczorek
.
Positive Linear Systems Consisting of $n$ Subsystems With Different Fr...
...[1], [4], [9], [11], [8], [
19
], [21] the survey paper [7] and references therein...
Carlos Lizama
.
An operator theoretical approach to a class of fractional order differ...
...d dspk (s) (t ¡ s)” ds, for 0 < ” < 1 (1.4) (see Podlubny [
12
])...
...Fractional equations of various types have proved to be useful in representing dierent phenomena in optics (light propagation through random media), transport of charge carriers and also in economics (a survey of applications can be found in Podlubny [
12
])...
Enzo Orsingher
,
et al.
Fractional pure birth processes
... of fractional integration and fractional dierentiation [52], a physical interpretation for the initial conditions in terms of the RiemannLiouville fractional derivatives of the unknown function has been suggested [27], the use of Caputo derivative in physical problems is perhaps more convenient since it allows using initial conditions expressed in terms of values of the unknown function and its integerorder derivatives [
50
]...
...where @ =@jxj (we adopt here the notation introduced in [54]) is a partial (with respect to spatial variable) symmetric Riesz derivative, which is dened as a halfsum of the left and rightsided RiemannLiouville derivatives [
50
, 51]:...
...Since the Caputo derivative of a constant is zero [2,
50
], for the auxiliary functiony(x;t) dened by equation (40) we obtain a problem with zero initial and boundary conditions similar to (41){(42):...
Igor Podlubny
,
et al.
Matrix approach to discrete fractional calculus II: Partial fractional...
...respectively. Note that for suciently smooth functions ’ for which ’(0) = 0 the left Caputo and RiemannLiouville derivatives coincide ([
12
], Formula (2.165)), i.e...
J. Kemppainen
,
et al.
Boundary Integral Solution of the TimeFractional Diffusion Equation
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(1049)
A class of fractional evolution equations and optimal controls
(
Citations: 29
)
JinRong Wang
,
Yong Zhou
Journal:
Nonlinear Analysisreal World Applications  NONLINEAR ANALREAL WORLD APP
, vol. 12, no. 1, pp. 262272, 2011
Discretetime fractional variational problems
(
Citations: 13
)
Nuno R. O. Bastos
,
Rui A. C. Ferreira
,
Delfim F. M. Torres
Journal:
Signal Processing
, vol. 91, no. 3, pp. 513524, 2011
Existence results for fractional impulsive integrodifferential equations in Banach spaces
(
Citations: 8
)
K. Balachandran
,
S. Kiruthika
,
J. J. Trujillo
Journal:
Communications in Nonlinear Science and Numerical Simulation  COMMUN NONLINEAR SCI NUMER SI
, vol. 16, no. 4, pp. 19701977, 2011
Studies on fractional order differentiators and integrators: A survey
(
Citations: 6
)
B. T. Krishna
Journal:
Signal Processing
, vol. 91, no. 3, pp. 386426, 2011
Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
(
Citations: 8
)
Ricardo Almeida
,
Delfim F. M. Torres
Journal:
Communications in Nonlinear Science and Numerical Simulation  COMMUN NONLINEAR SCI NUMER SI
, vol. 16, no. 3, pp. 14901500, 2011