On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

Abstract

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III).

Theory and Applications of Distinctive Conformable Triple Laplace and Sumudu Transforms Decomposition Methods

“…The authors in [19,21] recently introduced the single and double conformable Sumudu transform (CST) in 2019-20. Ibrahim et.al [36][37][38], have explored operator for symmetric conformable fractional derivative of complex variable and on quantum hybrid fractional conformable differential in a complex domain, in [39,40], on subclasses of analytic functions based on a quantum symmetric and the generalized wave dynamical equations based on time space symmetric differential equation operator, respectively, and Moreover, in [41], some fixed-point theorems for almost weak contraction in S-metric space via conformable fractional operator. In order to solve linear fractional partial differential equations in the conformable fractional derivative sense, we implement the conformable Triple Sumudu transform (CDST) due to the certain benefits of Sumudu transformation (ST) over Laplace Transformation (LT).…”

On Special Differential Subordinations Using Fractional Integral of Sălăgean and Ruscheweyh Operators

“…Quantum calculus has also been added to the studies for obtaining extensions of different types of operators. A quantum symmetric conformable differential operator is introduced in [5] as the generalization of known differential operators among which the Sȃlȃgean differential operator is included. Recently, in a new study [6], the authors have formulated a symmetric differential operator and its integral which has the Sȃlȃgean differential operator as the special case.…”

Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions

“…Newly, there is a quick development in the area of the QC and its application has appeared in discrete and continuous in mathematics and physics. In the field of geometric functions, theory [2], it brought a natural extension and vision of differential and integral operators (see [3][4][5][6]).…”