fractional calculus

The idea of calculus in fractional order is nearly as old as its integer counterpart. In a letter dated September 30th 1650, l’Hôpital posed the question of the meaning of $\\displaystyle{\\frac{d^{\\alpha}f}{dx^{\\alpha}}}$ if $\\displaystyle{\\alpha=\\frac{1}{2}}$ to Leibniz.There are different approaches to define calculus of fractional order. The following approaches are the most common and we can prove that they are equivalent

(1) Riemann-Liouville approach of fractional integration

(2) Grunwald-Letnikov approach of fractional differentiation

单词	FractionalCalculus
释义	fractional calculus The idea of calculus in fractional order is nearly as old as its integer counterpart. In a letter dated September 30th 1650, l’Hôpital posed the question of the meaning of $\\displaystyle{\\frac{d^{\\alpha}f}{dx^{\\alpha}}}$ if $\\displaystyle{\\alpha=\\frac{1}{2}}$ to Leibniz.There are different approaches to define calculus of fractional order. The following approaches are the most common and we can prove that they are equivalent (1) Riemann-Liouville approach of fractional integration (2) Grunwald-Letnikov approach of fractional differentiation
随便看	IndexOfTables index of tables IndexOfTheGroupOfCyclotomicUnitsInTheFullUnitGroup index of the group of cyclotomic units in the full unit group IndexSet index set IndexSetTheorem index set theorem IndirectProofOfIdentityTheoremOfPowerSeries indirect proof of identity theorem of power series IndiscreteTopology indiscrete topology InducedAlexandroffTopologyOnAPoset induced Alexandroff topology on a poset InducedPartialOrderOnAnAlexandroffSpace induced partial order on an Alexandroff space InducedRepresentation induced representation Induction induction Induction Induction and recursion on Cauchy reals InductionAxiom induction axiom Induction principles and dependent paths