Numerical Methods and Simulations in Fractal and Fractional Problems

Dear Colleagues,

The fast development of new technologies in almost all scientific fields and engineering applications has led to the investigation of challenging problems with high nonlinearities, singularities, parametric dependence, and randomness, so that analytical and rigorous solutions can not satisfy the increasing expectations. On the other hand, the many facilities offered by more and more sophisticated tools enable us to compute the numerical solution of complex problems with high accuracy and robustness. Special attention must be paid to those fractal-like problems or fractional problems where self-similarity, scale invariance, and fractional order of operators might add some extra difficulties to the numerical approximation methods.

The main aim of this Special Issue is to collect research papers to illustrate the numerical and computational methods in modeling, simulating, and implementing fractal and fractional problems.

Potential topics include but are not limited to:

• Non-Linear dynamics, nonlinear evolution equation
• Numerical method, computational method
• Partial differential equation
• Integral equation
• Ordinary differential equation
• Stochastic fractional partial differential equation models and applications
• Numerical and computational methods in fractional differential equations
• Quantitative theory of differential equations
• Fractional calculus-based control systems
• Complex dynamics—nonlinear dynamical systems
• Fractional calculus and its applications
• Finance and economy dynamics
• Fractals and chaos
• Biological systems and bioinformatics
• Image and signal processing
• Stability
• High-order numerical differential formulas for the fractional derivatives
• High-order numerical algorithms for fractional differential equations

Prof. Dr. Carlo Cattani
Prof. Dr. Mustafa Inc
Prof. Dr. Mehmet Ali Akinlar
Guest Editors

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 250 words) can be sent to the Editorial Office for assessment.

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.