Abstract
The holomorphic results for fractional differential operator formals have been established. The analytic continuation of these outcomes has been studied for the fractional differential formalwhere 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.
Highlights
Time scales calculus [1] cards us to teaching the dynamic equations, which contains both differences and differential equations, both of which are substantial in understanding applications
Holomorphic solution for some complex fractional classes is given in [5]- [7]
We generalize some properties by applying the concept of classic fractional derivative formal operator
Summary
Time scales calculus [1] cards us to teaching the dynamic equations, which contains both differences and differential equations, both of which are substantial in understanding applications. We use a majorant technique of analytic functions to prove the convergent of outcomes. The Riemann-Liouville fractional integral formal of the function φ of arbitrary order α > 0 is given by The Riemann-Liouville fractional differential formal of the function φ of arbitrary order α ∈ [0, 1) is given by
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