Recent Trends in Computational Physics with Fractional Applications

Dear Colleagues,

The field of computational physics has witnessed remarkable advancements over recent decades, with applications spanning a broad spectrum of scientific and engineering domains. Among these, fractional calculus has emerged as a powerful mathematical framework, extending traditional concepts of differentiation and integration to non-integer orders. This generalization has opened new avenues for modeling complex systems and processes characterized by memory effects, nonlocality, and anomalous dynamics, which are often beyond the scope of classical approaches.

Fractional calculus has proven its versatility and effectiveness across diverse areas, including fluid mechanics, viscoelastic materials, control theory, signal and image processing, financial modeling, biological systems, and nanotechnology. The integration of fractional calculus with computational methods has further expanded its applicability, enabling the simulation and analysis of intricate phenomena such as anomalous diffusion, fractional random walks, and complex dynamical systems.

Nonlinear partial differential equations (NLPDEs) remain central to many of these applications, describing fundamental physical processes across disciplines like fluid dynamics, plasma physics, solid mechanics, and quantum field theory. The inherent complexity and nonlinearity of these equations pose significant challenges for analytical solutions. Computational techniques, bolstered by methods like the inverse scattering transform, the Hirota bilinear method, Painlevé analysis, and other innovative approaches, have provided crucial tools for exploring and solving NLPDEs. The incorporation of fractional-order derivatives into these models has further enhanced their ability to capture real-world phenomena with higher accuracy and realism.

This Special Issue, titled “Recent Trends in Computational Physics with Fractional Applications”, aims to gather pioneering research that highlights the intersection of computational physics and fractional calculus. It seeks to showcase recent advancements in methodologies, novel applications, and theoretical insights that push the boundaries of this interdisciplinary field. Contributions focus on the development of new computational techniques, the exploration of fractional models in diverse scientific contexts, and the integration of fractional calculus into traditional and emerging areas of physics.

Dr. Lanre Akinyemi
Dr. Mehmet Senol
Dr. Solomon Manukure
Dr. Udoh Akpan
Guest Editors

Manuscript Submission Information

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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.

• stability analysis
• integral equations
• semi-analytical method
• traveling wave solutions
• analytical and numerical methods
• soliton theory and its applications
• fractional calculus and its applications
• ordinary and partial differential equations
• symmetry analysis and conservation laws
• mathematical modeling of flow in porous media
• multi-scale approaches to modeling wave phenomena
• high-order numerical differential formulas for fractional derivatives
• numerical and computational methods in fractional differential equations