Numerical Analysis and Iterative Methods for Fractional Differential Equations

Dear Colleagues,

Fractional calculus and fractional differential equations have become essential modelling tools in science and engineering for their enhanced ability to model complex systems with greater accuracy. By extending traditional calculus to non-integer orders, these mathematical tools provide a deeper understanding of systems characterized by memory effects, hereditary properties, and anomalous diffusion. Applications of fractional calculus span diverse fields such as control theory, signal processing, materials science, and bioengineering, where they improve the precision of models for viscoelastic materials, electrochemical processes, and biological systems. Due to the difficulty of obtaining exact solutions for fractional differential equations, numerical analysis plays a crucial role.

The aim of this Special Issue is to develop and analyze numerical, semi-numerical, and analytical schemes for approximating fractional differential equations, with applications across various science and engineering disciplines, including biomedical, mechanical, and chemical engineering. This Special Issue will also focus on the dynamical behaviors of numerical methods, offering insights into their convergence behaviors, stability, consistency, and efficiency.

We invite researchers to submit original articles presenting new developments and analyses of numerical techniques for solving fractional differential equations in engineering and applied sciences. Submissions should contribute to the advancement of numerical methods and their application to real-world problems, showcasing the potential of fractional calculus in enhancing model accuracy and understanding complex systems. Potential research topics include, but are not limited to, the following themes:

• Numerical methods and computational techniques for fractional differential equations;
• Stability and consistency of single and multi-step methods for fractional differential equations;
• Local and global convergence of iterative methods for nonlinear fractional equations;
• Fractional-order iterative-numerical schemes for nonlinear equations;
• Dynamical behavior of numerical schemes for fractional differential equations;
• Hybrid fractional-order numerical iterative schemes;
• Fractional-order numerical schemes based on artificial neural networks;
• Fractional-order numerical schemes for unconstrained optimizations problems;
• Iterative methods for fractional differential equations in finance and economics;
• Fractal behavior of fractional-order numerical schemes for nonlinear equations;
• Numerical methods for fractional-order epidemic models;
• Topological methods for fractional-order nonlinear equations;
• Fractional-order numerical schemes for systems of nonlinear equations;
• Numerical schemes for fractional nonlinear equations in physics, biology, and engineering;
• Numerical schemes for fuzzy fractional differential equations;
• Hybrid block methods for fractional-order differential equations;
• Applications of fractional differential equations in control systems and signal processing;
• Comparative analysis of fractional differential equation solvers;
• Error analysis and adaptive methods for fractional differential equations.

Dr. Mudassir Shams
Dr. Bruno Carpentieri
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.

• fractional differential equations
• fractional-order differential equations
• nonlinear fractional equations
• fuzzy fractional differential equations
• numerical methods and computational techniques
• stability and consistency
• local and global convergence
• iterative methods
• dynamical behaviors
• topological methods
• hybrid block methods
• comparative analysis
• error analysis and adaptive methods
• applications of fractional differential equations in systems and signal processing
• applications of nonlinear fractional equations in physics, biology, and engineering