Finite Difference Methods for Fractional and Stochastic Differential Equations

Dear Colleagues,

We are running a Special Issue on fractional and stochastic differential equations.

Fractional differential equations are a type of equation formed by changing integer order derivatives in a standard differential equation into fractional order derivatives. They are a valuable tool for describing processes with memory and hereditary properties, as well as non-locality and dynamic transmission processes of anomalous diffusion.

The importance of uncertainty modeling is recognized in scientific computing, and there has been a growing interest in applications of probabilistic methods. A stochastic differential equation is one in which one of the terms is a stochastic process, resulting in a solution which is also a stochastic process. Stochastic partial differential equations are used as models of transport phenomena in random media. They are also used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations.

Topics that are invited for submission include (but are not limited to):

• Multi-scale problems described by differential equations with highly oscillating coefficients;
• Study of wellposedness;
• Finite difference methods to solve these differential equations by approximating fractional derivatives;
• Modelling of real-life processes in science, engineering and finance through these differential equations;
• Numerical optimization of finite difference methods for these classes of differential equations.
• Analysis of properties (stability, consistency, convergence) of finite difference methods for fractional and stochastic partial differential equations.

Dr. Appanah Rao Appadu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• fractional differential equations
• stochastic differential equations
• analysis
• numerical methods
• applications