Related papers: Fractional Gamma process and fractional Gamma-subo…
In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where…
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…
We introduce and study a fractional version of the Skellam process of order $k$ by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order $k$ (FSPoK). An integral representation…
In this paper, the regularized trace formulas for a diffusion operator which include conformable fractional derivatives of order {\alpha} (0<{\alpha \leq 1}) is obtained.
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have obtained Krein representations of the…
We consider two fractional versions of a family of nonnegative integer valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As…
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…
In this paper, we introduce and study two time-changed variants of the generalized fractional Skellam process. These are obtained by time-changing the generalized fractional Skellam process with an independent L\'evy subordinator with…
A notion of evolutionary $\Gamma$-convergence of weak type is introduced for sequences of operators acting on time-dependent functions. This extends the classical definition of $\Gamma$-convergence of functionals due to De Giorgi. The…
We study quantum-fluctuation-driven fractionalized phases in the vicinity of altermagnetic order. First, the long-range magnetic orders in the vicinity of collinear altermagnetism are identified; these feature a non-coplanar "orbital…
We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.
In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of time variable and a negative power function of $\alpha-$stable random variable. The effect of parameters in the…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…