Existence Of Time-Scale Class Of Three Dimensional Fractional Differential Equations

The holomorphic results for fractional differential operator formals have been established. The analytic continuation of these outcomes has been studied for the fractional differential formal{partial derivative(alpha)v(p,z)/partial derivative p(alpha) = (sic) (p, z, v, partial derivative v/partial derivative z, partial derivative(2)v/partial derivative z(2)), alpha is an element of [0,1)v(a, z) = psi(z), in a proximity to z is an element of U,where U is the open unit disk. The benefit of such a problem is that a generalization of two significant problems: the Cauchy problem and the diffusion problem. Moreover, the analytic solution is given inside the open unit disk, this leads to discuss the solution geometrically. The upper bound of outcomes is determined by suggesting a majorant analytic function in U (for two functions characterized by a power series, a majorant is the summation of a power series with positive coefficients which are not less than the absolute values of the conforming coefficients of the assumed series). This technique is very useful in approximation theory.