Special functions as solutions to the Euler-Poisson-Darboux equation with a fractional power of the Bessel operator-Poisson-Darboux equation with fractional
derivatives in the form of a
power of the Bessel differential operator. Using
Information inequalities for characteristics of group-sequential test with groups of observations of random size of the
derivative of the
power function and establish the information-type inequalities relating that
derivative A fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type-sided fractional Bessel
derivatives on semi-axes of Gerasimov-Caputo type. We
derive explicit solutions
Information inequalities for characteristics of group-sequential test with groups of observations of random size of the
derivative of the
power function and establish the information-type inequalities relating that
derivative On the derivatives of set functions in matrix representation, obtained through matrix–vector multiplication. Many relations between the set
functions derivatives Double-layer potential of axially symmetric Helmholtz lowest term equation this
derivative a special
function unit is used. 3. The fundamental solution to the considered equation
A uniqueness theorem for linear elliptic equations with dominating derivative with respect to z with analytic coefficients whose senior
derivative is the n-th
power of the Cauchy–Riemann operator.
Hardy type inequalities for fractional integrals and derivatives of Riemann–Liouville–Liouville fractional integrals and
derivatives in the case when the weight
function have
power and logarithmic
Locally Most Powerful Group-Sequential Tests with Groups of Observations of Random Size: Finite Horizon characteristics: its error probability of the first type, the
derivative of its
power function at θ = θ0
Fractional Bessel integrals and derivatives on semi-axesIn this paper we study fractional
powers of the Bessel differential operator. The fractional
powers