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
Molecular magnetism is reaching a degree of development that will allow for the rational design of sophisticated systems.Among these,here we will focus on those that display single-molecule magnetic behaviour,i.e.clas...Molecular magnetism is reaching a degree of development that will allow for the rational design of sophisticated systems.Among these,here we will focus on those that display single-molecule magnetic behaviour,i.e.classical memories,and on magnetic molecules that can be used as molecular spin qubits,the irreducible components of any quantum technology.Compared with candidates developed from physics,a major advantage of molecular spin qubits stems from the power of chemistry for the tailored and inexpensive synthesis of new systems for their experimental study;in particular,the so-called lanthanoid-based single-ion magnets,which have for a long time been one of the hottest topics in molecular magnetism.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.
基金funded by the EU(ERC Advanced Grant SPINMOL and ERC Consolidator Grant DECRESIM),the Spanish MINECO(grant MAT2014-56143-R,CTQ2014-52758-P and Unidad de Excelencia María de Maeztu MDM-2015-0538 granted to ICMol)the Generalitat Valenciana(Prometeo and ISIC Programmes of Excellence)+1 种基金A.G.-A.acknowledges funding by the MINECO(Ramón y Cajal contract)J.J.B.acknowledge the Blaise Pascal International Chair for financial support.J.J.B.also thanks the Spanish MECD for an FPU predoctoral grant.L.E.M.acknowledges the Generalitat Valenciana for a VALi+D predoctoral grant.S.C.-S.acknowledges the Generalitat Valenciana for a VALi+D postdoctoral grant.
文摘Molecular magnetism is reaching a degree of development that will allow for the rational design of sophisticated systems.Among these,here we will focus on those that display single-molecule magnetic behaviour,i.e.classical memories,and on magnetic molecules that can be used as molecular spin qubits,the irreducible components of any quantum technology.Compared with candidates developed from physics,a major advantage of molecular spin qubits stems from the power of chemistry for the tailored and inexpensive synthesis of new systems for their experimental study;in particular,the so-called lanthanoid-based single-ion magnets,which have for a long time been one of the hottest topics in molecular magnetism.
