The Lie symmetry method is applied to derive the point symmetries for N-dimensional fractional heat equation. We find that numbers of and brackets are reduced significantly as compared integer order all dimensions. In fact linear equation number solution equal product space dimension, whereas case, it half on dimension. algebras equations mentioned using subsequent computations by inspection. I...

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...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

This paper presents a simple but effective approach for the removal of additive white Gaussian noise from digital images. In our approach, a generalization of a linear heat equation, obtained by replacing time derivative to a fractional time derivative of order between 1 and 2 has been used and a pixel by pixel technique applied. The choice of order of fractional time derivative has been made f...