Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its u...Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.展开更多
文摘Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.
