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Synchronization and dynamics of modified fractional order Kawasaki disease model with chaos stability control. [PDF]

Sci Rep
Nisar KS, Farman M, Jamil K, Hincal E, Sambas A.   +4 more
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Fractional Derivative and Fractional Integral

2018
For every α > 0 and a local integrable function f(t), the right FI of order α is defined: $$\displaystyle{ }_aI_t^\alpha f(t) = \displaystyle\frac {1}{\Gamma (\alpha )}\displaystyle\int _a^t(t - u)^{\alpha - 1}f(u)du,\qquad-\infty \le a < t < \infty .$$
Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado   +2 more
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Fractional derivatives, fractional integrals and electromagnetic theory

1999 International Conference on Computational Electromagnetics and its Applications. Proceedings (ICCEA'99) (IEEE Cat. No.99EX374), 2003
Summary form only given. Fractional derivatives/integrals are mathematical operators involving differentiation/integration to arbitrary noninteger orders-orders that may be fractional or even complex. These operators, which possess interesting mathematical properties, have been studied in the field of fractional calculus.
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a-times integrated semigroups and fractional derivation

Forum Mathematicum, 2002
The work is devoted to the \(\alpha\)-times integrated semigroups and functional calculus which is related to smooth distribution semigroups. The functional calculus for \(\alpha\)-times integrated semigroups is obtained by applying the fractional integration and derivation to the vector-valued Laplace transform.
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Approximations of fractional integrals and Caputo fractional derivatives

Applied Mathematics and Computation, 2006
In a series of recent papers [see \textit{K. Diethelm, A. D. Freed} and \textit{N. J. Ford}, Numer. Algorithms 36, No. 1, 31--52 (2004; Zbl 1055.65098)], and the references cited therein], the reviewer and his collaborators have proposed and analysed a numerical scheme for the approximation of \(J^\alpha\), the Riemann-Liouville fractional integral of ...
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Transients of fractional-order integrator and derivatives

Signal, Image and Video Processing, 2012
Although fractional-order differentiation is generallyconsidered as the basis of fractional calculus, we demonstrate in this paper that the real basis is in fact fractional-order integration, mainly because definition and properties of fractional differentiation rely deeply on fractional integration.
J. C. Trigeassou, N. Maamri, J. Sabatier, A. Oustaloup   +3 more
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General fractional integrals and derivatives and their applications

Physica D: Nonlinear Phenomena, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Review on Integral Transforms of Fractional Integral and Derivative

International Academic Journal of Science and Engineering, 2022
In this paper, we present a review of the integral transformations of fractional calculus, namely the Riemann-Liouville integral, the Riemann-Liouville derivative, and the Caputo derivative.
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Fractional derivatives: integral representations and generalized polynomials

2004
Summary: We show that the use of functions associated with generalized forms of Hermite polynomials provide a natural tool for the solution of partial differential equations involving fractional derivatives. Within such a context we clarify the meaning of exponential operators with fractional derivatives and discuss alternative definitions based on ...
DATTOLI G, CESARANO C, RICCI, Paolo Emilio, VAZQUEZ L.   +3 more
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