Results 41 to 50 of about 374,024 (252)
Fractional Statistical Mechanics [PDF]
Chaos. Vol.16. No.3. (2006) 033108, 2007 The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives ...
arxiv +1 more source
A Modified Fractional Derivative and its Application to Fractional Vibration Equation [PDF]
, 2016 In this paper, a new modified definition of the fractional derivative is presented. The Laplace transform of the modified fractional derivative involves the initial values of the integer-order derivatives, but does not involve the initial values of the ...
Duan, Jun-Sheng
core +2 more sources
Advances in Difference Equations, 2018 Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Shadab +2 more
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Axioms, 2023 In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem of a second-order differential equation containing a fractional derivative operator.
Ludmila Kiryanova, Tatiana Matseevich
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No Nonlocality. No Fractional Derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation.
2018. Vol.62. P.157-163, 2018 The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point.
arxiv +1 more source
Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]
Journal of Mathematics, 2021 In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.
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Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales [PDF]
Abstract and Applied Analysis, 2013 -Laplace transform, fractional -power function, -Mittag-Leffler function, fractional -integrals, and fractional -differential on time scales are defined. Some of their properties are discussed in detail. After then, by using Laplace transform method, the existence of the solution and the dependency of the solution upon the initial value for Cauchy-type
Ling Wu, Jiang Zhu
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The unified Riemann-Liouville fractional derivative formulae
Tamkang Journal of Mathematics, 2005 In this paper, we obtain two unified fractional derivative formulae. The first involves the product of two general class of polynomials and the multivariable $H$-function. The second fractional derivative formula also involves the product of two general class of polynomials and the multivariable $H$-function and has been obtained by the application of ...
R. C. Soni, Deepika Singh
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The Fractional Chapman-Kolmogorov Equation [PDF]
Modern Physics Letters B 21 (2007) 163-174, 2007 The Chapman-Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman-Kolmogorov equation is obtained.
arxiv +1 more source
Fractional Fokker-Planck Equation for Fractal Media [PDF]
Chaos 15 (2005) 023102, 2006 We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation).
arxiv +1 more source