Estimates of Classes of Generalized Special Functions and Their Application in the Fractional $\left(k,s\right)$-Calculus Theory

Abstract

In this article, we aim to develop new k , s -fractional integral and differential operators containing S -functions as kernels in a form of generalized k -Mittag-Leffer functions. We also set up various properties of such operators. Furthermore, we consider a variety of implications of the major outcomes that will be very useful in the implementation of scientific, engineering, and technical problems.

Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional q-Difference Operator

“…Srivastava et al [24] studied q-Noor integral operators and some of their applications. The q-calculus theory in a fractional sense and its real applications in the geometric class of functions of complex analysis and related fields are investigated in [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators

“…Therefore, for a function g in the class S n,Ψ q,λ (µ, ζ), expressed by (23), by using the inequality (17), we obtain…”

“…In [16], Kanas and Raducanu introduce q-analogues of the Ruscheweyh differential operators and establish some convolution properties of some normalized analytic functions. In [17], Darus et al study a q-analogue of some operator by using q-hypergeometric functions. Moreover, authors of [18][19][20][21] apply properties of the q-difference operator to discuss subclasses of complex analytic functions.…”

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain

“…Kanas and Raducanu established some convolution properties of a few normalized analytic functions in [15] and introduced q-analogues of the Ruscheweyh differential operators. Using q-hypergeometric functions, Darus et al examined a q-analogue of a certain operator in [16]. Furthermore, the writers of [17][18][19][20] used the q-difference operator's characteristics and defined different subclasses of complex analytical functions.…”