We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential equations of mathematical physics. Fractionality is obtained by substituting the ordinary integer-order derivative with the Caputo fractional ...

Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-...

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. Statistical mechanics of fractional generaliz...

Abstract In this paper, we study the following Kirchhoff-type Schrödinger-Poisson systems in $\mathbb{R}^{2}$ R 2 : $$ \textstyle\begin{cases} - (a+b\int _{{\mathbb{R}}^{2}} \vert \nabla u ^{2}\,\mathrm{d}x ) \Delta u+V(x)u+\mu \phi u=f(u),\quad x\in {\mathbb{R}}^{2}, \...