SYMMETRICALLY CONFORMABLE FRACTIONAL DIFFERENTIAL OPERATORS BY COMPUTATIONAL NUMERICAL MODELING WITH SPECIAL FUNCTION

Abstract

The [Formula: see text]-convoluted operators related to the [Formula: see text]-Whittaker function, confluent hypergeometric function of the first kind, have been developed using the [Formula: see text]-symbol calculus in which this sort of calculus presents a generalization of the gamma function. [Formula: see text]-symbol fractional calculus is employed to generalize and extend many differential and integral operators of fractional calculus. Based on this premise, a new geometric formula for normalized functions in the symmetric domain known as the open unit disk using the conformable fractional differential operator has been presented in this study. Thus, our technique entails investigating the most well-known geometric properties of this new operator, such as the subordination features and coefficient bounds so that the theory of differential subordination can be adjusted accordingly. By means of this technique, numerical results have been investigated for the proposed method. To this end, a few prominent corollaries of our primary findings as standout instances have been pointed out based on the positivity of the solutions, computational and numerical analyses.