Editorial for the Special Issue “Operators of Fractional Calculus and Their Multidisciplinary Applications”

Srivástava, H. M.

doi:10.3390/fractalfract7050415

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…The operators of q-fractional calculus have been addressed and effectively implemented in a number of recent and continuing publications; see [36]. From the fractional calculus q-Pochhammer symbol, several writers have expanded the notions of fractional q-integral and fractional q-derivative by proposing many different lower limits of integration.…”

Section: Discussionmentioning

confidence: 99%

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

Khan,

Tawfiq

et al. 2023

Fractal Fract

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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, Λβ,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.

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Section: Discussionmentioning

confidence: 99%

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

Khan,

Tawfiq

et al. 2023

Fractal Fract

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“…Fractional differential calculus now plays a significant part in the diagnosis of diseases in the medical field, (see [57][58][59][60]). For the area of complex fractional differential operators, see the following articles [61][62][63].…”

Section: Applicationmentioning

confidence: 99%

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Khan,

AbaOud

2024

Fractal Fract

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Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.

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Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

Srivastava,

Shaba,

Ibrahim

et al. 2024

Bulletin des Sciences Mathématiques

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Editorial for the Special Issue “Operators of Fractional Calculus and Their Multidisciplinary Applications”

Abstract: This Special Issue of the MDPI journal, Fractal and Fractional, on the subject area of “Operators of Fractional Calculus and Their Multidisciplinary Applications” consists of 19 peer-reviewed papers, including some invited feature articles, originating from all over the world [...]

Cited by 3 publications

References 23 publications

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

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