Related papers: Stationarity-conservation laws for certain linear …
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications:…
Starting from the Riemann-Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…
The fractional Leibniz rule is generalized by the Coifman-Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite…
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…
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
In this short communication, we show that the validity of the Leibniz rule for a fractional derivative on a coarse-grained medium brings about a modified chain rule, in agreement with alternative versions of fractional calculus. We compare…
A type of fractional derivative, referred to as \alpha-derivative, is studied. The \alpha-derivative of fractional type obeys Leibnitz rule. Based on the definition of \alpha-derivative the operations of analysis and differential geometry…
This manuscript is dedicated to prove a new inequality that involves an important case of Leibniz rule regarding Riemann-Liouville and Caputo fractional derivatives of order $\alpha\in(0,1)$. In the context of partial differential…
In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff…
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.…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…