Numerical Modelling and Analysis of Fractional-Order Partial Differential Equations: Methods and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".
Deadline for manuscript submissions: 30 April 2026 | Viewed by 12
Special Issue Editor
2. Escuela Politécnica Superior de Zamora, Universidad de Salamanca, Campus Viriato, 49029 Zamora, Spain
Interests: numerical analysis; adaptive stepsize algorithms; numerical solution of differential equations; chebyshev approximations; block methods; computational mathematics
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Fractional-order partial differential equations (PDEs) have emerged as a powerful mathematical tool in scientific computing due to their ability to model memory and hereditary properties in complex systems. These equations provide deeper insights into various phenomena, including diffusion processes, electrodynamics, control theory, and fluid dynamics. Their applications span multiple disciplines, such as engineering, physics, and biological systems, offering a richer framework compared to classical differential equations.
Despite their promising potential, solving fractional-order PDEs poses significant challenges due to their non-local properties and complex computational requirements. Analytical solutions are often limited, necessitating the development of efficient numerical techniques for accurate and reliable solutions. This Special Issue will focus on innovative methods for the numerical modelling of fractional-order PDEs, emphasizing robust computational strategies, stability analysis, and real-time applications in science and engineering.
By exploring high-order numerical schemes, adaptive algorithms, and parallelization strategies, this Special Issue aims to foster interdisciplinary collaboration and bridge the gap between theoretical advances and practical applications. Topics such as bifurcation analysis, control strategies, and pattern formation will offer deeper insights into the dynamics of systems governed by fractional-order PDEs.
This Special Issue aims to bridge theoretical advancements with practical implementations, providing valuable insights into the numerical modelling of fractional-order PDEs. Researchers in applied mathematics, computational physics, control theory, interdisciplinary scientists dealing with complex systems, and industry experts are invited to contribute their latest findings and innovative approaches to this growing field.
Prof. Dr. Higinio Ramos
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.
Keywords
- numerical methods for fractional-order PDEs
- computational techniques for fractional calculus
- high-order accuracy schemes for fractional differential equations
- stability and convergence analysis of numerical solutions
- scientific computing applications in engineering and physics
- fractional-order modelling in biological and chemical systems
- computational fluid dynamics and water wave phenomena
- applications of fractional pdes in control theory and dynamical systems
- robust algorithms for large-scale fractional differential equations
- adaptive mesh refinement and parallel computing for fractional PDEs
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.
Further information on MDPI's Special Issue policies can be found here.
