Special Issue "Advanced Numerical Methods for Fractional Differential Equations"

Submission Deadline: 15 September 2022
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Guest Editors
Prof. Qasem M. Al-Mdallal, UAE University, UAE
Prof. Thabet Abdeljawad, Prince Sultan University, Saudi Arabia
Prof. Fahd Jarad, Çankaya University, Turkey


Fractional calculus, which is defined by the branch of calculus that generalizes the derivative of a function to non-integer order, is born in 1695 in a letter written by Gottfried Wilhelm Leibniz to Guillaume de l'Hôspital. Later, more great scientists contributed to the development of the field of fractional operators such as: Liouville, Riemann, and Laurent. Additionally, several theoretical studies on fractional calculus were reported in the 19th century.


In recent years, the area of Fractional Calculus received a huge interest from the scientific community especially mathematicians, physicians, and engineers. This interest is due to the usage of fractional calculus in the mathematical modeling of systems with memory effects. Consequently, the importance of fractional calculus appears in many applications in various fields such as biology, chemistry, networks, fractal geometry, fluid dynamics, control theory, medicine, and finance, etc. 


The main target of this special issue is to create a multidisciplinary forum of discussions on the most recent results in this field of research. More precisely, we will focus on recent advanced numerical studies on Fractional Differential. In addition, the well-developed analysis of existing numerical algorithms in terms of efficiency, applicability, convergence, stability and accuracy is of importance. A discussion of nontrivial numerical examples is encouraged.


Potential topics include, but are not limited to:


•     Numerical methods for Fractional differential equations.

•     Numerical methods for Fractional difference equations.

•     Numerical methods for Fractional integro-differential equations.

•     Mathematical control theory.

•     Any Related topics

Published Papers
  • Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials
  • Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are solved with the help of… More
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