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School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China
Department of Mathematics, Dongguk University, Wise Campus, Gyeongju 38066, Republic of Korea
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Fractional Calculus, Symmetry Phenomenon and Probability Theory for PDEs, and ODEs

Abstract submission deadline
28 February 2025
Manuscript submission deadline
30 April 2025
Viewed by
793

Topic Information

Dear Colleagues,

This topic aims to delve into the frontier research of fractional calculus, symmetry phenomenon, probability theory, and fractional differential equations. Fractional calculus, as an essential branch of modern mathematics, provides powerful tools for modeling and analyzing complex systems. Fractional differential equations have widespread applications in physics, engineering, and other fields. This topic will gather the latest research achievements in this area, promote academic exchange and cooperation, and drive the development of fractional calculus and fractional differential equations in both theory and application. Potential topics include but are not limited to the following:

  • Stability analysis of fractional partial differential equations in infinite dimensional dynamical systems;
  • Bifurcation phenomena in fractional partial differential equations within infinite dimensional dynamical systems;
  • Fractional stochastic partial differential equations for complex real-world problems;
  • Applications of fractional calculus in physical modeling;
  • Recent advances in complex system analysis using fractional differential equations;
  • Cross-research between fractional calculus and nonlinear science;
  • Explorations in the application of fractional calculus in signal and image processing.

Prof. Dr. Renhai Wang
Prof. Dr. Junesang Choi
Topic Editors

Keywords

  • fractional calculus
  • fractional differential equations
  • modeling of complex systems
  • stability analysis
  • numerical solution methods
  • nonlinear science
  • physical modeling
  • optimization strategies

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
AppliedMath
appliedmath 		- - 2021 33.2 Days CHF 1000 Submit
Axioms
axioms 		1.9 - 2012 21 Days CHF 2400 Submit
Fractal and Fractional
fractalfract 		3.6 4.6 2017 20.9 Days CHF 2700 Submit
Mathematical and Computational Applications
mca 		1.9 - 1996 28.8 Days CHF 1400 Submit
Mathematics
mathematics 		2.3 4.0 2013 17.1 Days CHF 2600 Submit
Symmetry
symmetry 		2.2 5.4 2009 16.8 Days CHF 2400 Submit

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Published Papers (1 paper)

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25 pages, 1991 KiB  
Article
Chebyshev Pseudospectral Method for Fractional Differential Equations in Non-Overlapping Partitioned Domains
by Shina Daniel Oloniiju, Nancy Mukwevho, Yusuf Olatunji Tijani and Olumuyiwa Otegbeye
AppliedMath 2024, 4(3), 950-974; https://doi.org/10.3390/appliedmath4030051 - 2 Aug 2024
Viewed by 383
Abstract
Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when [...] Read more.
Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when dealing with such problems. This study proposes a novel multi-domain pseudospectral method based on the first kind of Chebyshev polynomials and the Gauss–Lobatto quadrature for fractional initial value problems.The proposed technique involves partitioning the problem’s domain into non-overlapping sub-domains, calculating the fractional differential operator in each sub-domain as the sum of the ‘local’ and ‘memory’ parts and deriving the corresponding differentiation matrices to develop the numerical schemes. The linear stability analysis indicates that the numerical scheme is absolutely stable for certain values of arbitrary non-integer order and conditionally stable for others. Numerical examples, ranging from single linear equations to systems of non-linear equations, demonstrate that the multi-domain approach is more appropriate, efficient and accurate than the single-domain scheme, particularly for problems with long-term dynamics. Full article
(This article belongs to the Topic Fractional Calculus, Symmetry Phenomenon and Probability Theory for PDEs, and ODEs)
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