41 citations · 120 across the 8 of their papers we have counts for
8 papers
A novel numerical technique used in the solution of ordinary differential equations with a mixture of integer and fractional derivatives
Jacek S. Leszczynski, Tomasz Blaszczyk
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to o…
Numerical treatment of an initial-boundary value problem for fractional partial differential equations
Mariusz Ciesielski, Jacek Leszczynski
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to…
Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator
Mariusz Ciesielski, Jacek Leszczynski
In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a ste…
Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative
Mariusz Ciesielski, Jacek Leszczynski
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffus…
Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions
Jacek S. Leszczynski
Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multip…
Numerical simulations of anomalous diffusion
Mariusz Ciesielski, Jacek Leszczynski
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional…