相关论文: On Fractional Kinetic Equations
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…
We extend Noether's symmetry theorem to the fractional Riemann-Liouville integral functionals of the calculus of variations recently introduced by El-Nabulsi.
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
In a recent paper (Abe S 2013 Phys. Rev. E 88 022142), a variational principle has been formulated for spatiotemporally-fractional Fokker-Planck equations and applied to derivations of their approximate analytic solutions based on the…
In this paper, we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving…
In the article [B.J.West, Exact solution to fractional logistic equation, Physica A: Statistical Mechanics and its Applications 429 (2015) 103-108], the author has obtained a function as the solution to fractional logistic equation (FLE).…
This paper is devoted to hydrodynamic limits of linear kinetic equations when the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a Maxwellian distribution. We show that the long time/small mean…
This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
This paper combines probability theory and fractional calculus to derive a novel integral representation of the three-parameter Mittag-Leffler function or Prabhakar function, where the three parameters are combinations of four base…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the…
The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Levy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and…
We consider a singular fractional differential equation involving generalized Katugampola derivative and obtain the existence and uniqueness of its solution. A scheme for uniformly approximating solution is constructed by using Picard…
This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses…
A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function that can be expanded by Taylor series, we show that D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD is applied for some functions in…
While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…
In this paper, we investigate the fundamental solution of the fractional Fokker-Planck equation. Utilizing the Littlewood-Paley decomposition technology, we present a concise proof of the pointwise estimate for the fundamental solution.
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…