A fractional power approach to fractional calculus
A theory of fractional powers of operators on an arbitrary Fréchet space is discussed. As special cases, multivariable fractional integrals and derivatives defined on certain spaces of test functions and generalised functions are obtained. In particular, properties of the two- dimensional Riesz fractional integral are determined and used to solve a distributional initial value problem involving the wave operator.
fractional powers of operators on an arbitrary Fréchet space
multivariable fractional integrals and derivatives
two-dimensional Riesz fractional integral
distributional initial value problem involving the wave operator
scientific article; zbMATH DE number 4161492
scientific article