This paper introduces and studies a new class of analytic p-valent functions in the open symmetric unit disc involving Sălăgean-type q-difference operator. Furthermore, we present several interesting subordination results, coefficient inequalities, fractional q-calculus applications, distortion theorems.

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractio...

Fractal and Fractional are two words referring to some characteristics and fundamental problems which arise in all fields of science and technology. These problems are characterized by having some non-integer order features. Fractals are geometrical objects with non-integer dimension, while fractional is the non-integer order of differential operators. Fractals and fractional calculus have been...

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests in recent years. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory (see e.g...

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of VolterraFredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. MSC: 34K37 • 34A08 • 47H10

Three-dimensional bicovariant differential calculus on the quantum group SU q (2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U (1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus on SU q (2) is uniquely defined. A non-...

Using the derivative operators’ q-analogs values, a wide variety of holomorphic function subclasses, q-starlike, and q-convex functions have been researched examined. With aid fundamental ideas from theory q-calculus operators, we describe new q-operators harmonic Hϱ,χ;qγF(ϖ) in this work. We also define subclass related to Janowski q-analog Le Roy-type Mittag–Leffler functions. Several importa...