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This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coefficient bounds, Zalcman inequalities, and both Hankel and Toeplitz determinants for the new version of starlike functions are investigated. It is worth mentioning that most of the determined inequalities are sharp with the support of relevant extremal functions. [ABSTRACT FROM AUTHOR]

In this paper, we study a new filtration class MF α , β μ , associated with the filtration of infinitesimal generators, by using the nonlinear fractional differential operator and study certain properties, like sharp Fekete–Szegö inequalities and filtration problems. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of quantum (or q -) calculus and define a q -analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly q -starlike and q -convex functions associated with a new generalized conic domain, Λ β , q , γ . To begin establishing our key conclusions, we explore several novel lemmas. Furthermore, we employ these lemmas to explore some important features of these two classes, for example, inclusion relations, coefficient bounds, Fekete–Szego problem, and subordination results. We also highlight many known and brand-new specific corollaries of our findings. [ABSTRACT FROM AUTHOR]

This article investigates inequalities for certain types of strongly convex functions by applying q-h-integrals. These inequalities provide the refinements of some well-known results that hold for (α , m) - and (ℏ - m) -convex and related functions. Inequalities for q-integrals are deducible by vanishing the parameter h. Some particular cases are discussed after proving the main results. [ABSTRACT FROM AUTHOR]

The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, and Fekete–Szegö inequalities, for this novel family of bi-univalent functions. It is worthy of note that almost all the results are sharp, and their corresponding extremal functions are presented. In addition, some special cases are demonstrated to show the validity of our findings. [ABSTRACT FROM AUTHOR]

This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially (α , h − m) − p -convexity is utilized frequently. In addition, a fractional Hadamard type inequality which shows the upper and lower bounds of k-integral operators simultaneously is presented. The results are directly linked with the results of many published articles. [ABSTRACT FROM AUTHOR]

Chemical graph theory (CGT) is a field of mathematical science that applies classical graph theory to chemical structures and processes. Chemical graphs are the principal data format used in cheminformatics to illustrate chemical interactions. Several researchers have addressed boundary-value problems using star graphs. Star graphs were used since their method requires a central point linked to other vertices but not to itself. Our objective is to expand the mechanism by introducing the idea of an isobutane graph that has the chemical formula C 4 H 10 and CAS number 75-28-5. By using the appropriate fixed point theory findings, this paper investigates the existence of solutions to fractional boundary value problems of Caputo type on such graphs. Additionally, two examples are provided to strengthen our important conclusions. [ABSTRACT FROM AUTHOR]

This paper focuses on the approximate controllability of Hilfer fractional neutral Volterra integro-differential inclusions via almost sectorial operators. Almost sectorial operators, fractional differential, Leray-Schauder fixed point theorem and multivalued maps are used to prove the result. We start by emphasizing the existence of a mild solution and demonstrate the approximate controllability of the fractional system. In addition, an example is presented to demonstrate the principle. [ABSTRACT FROM AUTHOR]

The work presented in this article is composed of 2-dimensional groundwater flow simulations for fractured porous media with different aperture of fractures by using the Analytic Element Method. In order to investigate the flow behavior and its effect on fractures, we considered different systems of fractures with varying apertures, hydraulic conductivities and orientations in the presence of uniform flow field and a well. We also introduced the matrix method to solve the problems for which the unknown coefficients are obtained from the discharge potential of all the elements present in the systems. The numerical solution of the prescribed problem is based on a series expansion, while the influence of each fracture is expressed in a series that satisfy Laplace's equation. [ABSTRACT FROM AUTHOR]

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaining traction in current fields, including computational fluid dynamics, computational probability, data assimilation, statistics, numerical analysis, and image and signal processing. In this paper, using q-Hermite polynomials, we define a new subclass of bi-univalent functions. We then obtain a number of important results such as bonds for the initial coefficients of | a 2 | , | a 3 | , and | a 4 | , results related to Fekete–Szegö functional, and the upper bounds of the second Hankel determinant for our defined functions class. [ABSTRACT FROM AUTHOR]

The technological development in wind energy conversion systems (WECSs) places emphasis on the injection of wind power into the grid in a smoother and robust way. Sliding mode control (SMC) has proven to be a popular solution for the grid-connected WECS due to its robust nature. This paper reviews the enhancement trends in the integer-order SMC (IOSMC) and fractional-order SMC (FOSMC) schemes reported in reputed journals over the last two decades. This work starts with a mathematical description of the wind turbine, generators, grid, and SMC and its variants available in literature. A comprehensive literature review is tabulated that includes the proposed errors, sliding surfaces, typologies, and major outcomes. Moreover, a comparative analysis of the integer-order and fractional-order SMC and its variants is also presented in this paper. This paper will provide insight for the researcher working in the WECS and will serve them in the selection and exploration of the most appropriate control schemes for quality wind power extraction. The concise mathematical proofs of the IOSMC, FOSMC and their variants will also serve the researchers in selecting the relevant sliding surfaces control laws for their research tasks. This paper also provides a comparative analysis of IOSMC, FOSMC, and fuzzy-FOSMC in terms of chattering reduction, robustness, and computational complexities using mathematical theories, simulation carried out in Matlab/Simulink, and a processor in the loop (PIL)-based experimental environment. [ABSTRACT FROM AUTHOR]

In this article we have defined two new subclasses of analytic functions k − S q [ A , B ] and k − K q [ A , B ] by using q-difference operator in an open unit disk. Furthermore, the necessary and sufficient conditions along with certain other useful properties of these newly defined subclasses have been calculated by using q-difference operator. [ABSTRACT FROM AUTHOR]

In recent years, special functions such as Bessel functions have been widely used in many areas of mathematics and physics. We are essentially motivated by the recent development; in our present investigation, we make use of certain conic domains and define a new class of analytic functions associated with the Dini functions. We derive inclusion relationships and certain integral preserving properties. By applying the Bernardi-Libera-Livingston integral operator, we obtain some remarkable applications of our main results. Finally, in the concluding section, we recall the attention of curious readers to studying the q-generalizations of the results presented in this paper. Furthermore, based on the suggested extension, the (p , q) -extension will be a relatively minor and unimportant change, as the new parameter p is redundant. [ABSTRACT FROM AUTHOR]

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant H 3 (1) for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, coefficient estimates, etc. [ABSTRACT FROM AUTHOR]