Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

Karthikeyan, Kadhavoor R.; Murugusundaramoorthy, Gangadharan

doi:10.3390/fractalfract8030131

Cited by 4 publications

(1 citation statement)

References 34 publications

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“…This has paved the way for the utilization of multiplicative calculus in various aspects of practical life. Example application areas are biomedical image analysis [5], economics [6], time-scale theory [7], chemical engineering [8], processing of real-world signals [9], fractional dynamical systems [10], and digital image interpolation [11]. A recent study developed an analytical model to predict COVID-19 spread by incorporating multiplicative calculus into machine learning [12].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

Kosunalp,

Bas,

Kosunalp

2024

Symmetry

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The field of multiplicative analysis has recently garnered significant attention, particularly in the context of solving multiplicative differential equations (MDEs). The symmetry concept in MDEs facilitates the determination of invariant solutions and the reduction of these equations by leveraging their intrinsic symmetrical properties. This study is motivated by the need for efficient methods to address MDEs, which are critical in various applications. Our novel contribution involves leveraging the fundamental properties of orthogonal polynomials, specifically Laguerre polynomials, to derive new solutions for MDEs. We introduce the definitions of Laguerre multiplicative differential equations and multiplicative Laguerre polynomials. By applying the power series method, we construct these multiplicative Laguerre polynomials and rigorously prove their basic properties. The effectiveness of our proposed solution is validated through illustrative examples, demonstrating its practical applicability and potential for advancing the field of multiplicative analysis.

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Section: Introductionmentioning

confidence: 99%

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

Kosunalp,

Bas,

Kosunalp

2024

Symmetry

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Applications of Mittag–Leffler Functions on a Subclass of Meromorphic Functions Influenced by the Definition of a Non-Newtonian Derivative

Breaz,

Karthikeyan,

Murugusundaramoorthy

2024

Fractal Fract

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In this paper, we defined a new family of meromorphic functions whose analytic characterization was motivated by the definition of the multiplicative derivative. Replacing the ordinary derivative with a multiplicative derivative in the subclass of starlike meromorphic functions made the class redundant; thus, major deviation or adaptation was required in defining a class of meromorphic functions influenced by the multiplicative derivative. In addition, we redefined the subclass of meromorphic functions analogous to the class of the functions with respect to symmetric points. Initial coefficient estimates and Fekete–Szegö inequalities were obtained for the defined function classes. Some examples along with graphs have been used to establish the inclusion and closure properties.

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On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations

Shams

2024

Mathematics

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Fractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predictions regarding outcomes across a range of applications where these problems are effectively addressed. This research introduces a novel hybrid multiplicative calculus-based parallel method for solving complex nonlinear models in engineering. To speed up the method’s rate of convergence, we utilize a second-order multiplicative root-finding approach as a corrector in the parallel framework. Using rigorous theoretical analysis, we illustrate how the hybrid parallel technique based on multiplicative calculus achieves a remarkable convergence order of 12, indicating its effectiveness and efficiency in solving complex nonlinear equations. The intrinsic stability and consistency of the approach—when applied to nonlinear situations—are clearly indicated by the symmetry seen in the dynamical planes for various parameter values. The method’s symmetrical behavior indicates that it produces accurate findings under a range of scenarios. Using a dynamical system procedure, the ideal parameter values are systematically analyzed in order to further improve the method’s performance. Implementing the aforementioned parameter values using the parallel approach yields very reliable and consistent outcomes. The method’s effectiveness, reliability, and consistency are evaluated through the analysis of numerous nonlinear engineering problems. The analysis provides a detailed comparison with current techniques, emphasizing the benefits and potential improvements of the novel approach.

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Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

Cited by 4 publications

References 34 publications

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

Applications of Mittag–Leffler Functions on a Subclass of Meromorphic Functions Influenced by the Definition of a Non-Newtonian Derivative

On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations

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