On the multiplicative Legendre equation

Goktas, Sertac

doi:10.1080/16583655.2022.2119554

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…It can be easily demonstrated that the positive and continuous function f(t) on the interval [0, ∞) can be expanded in a series of Laguerre polynomials [19].…”

Section: Multiplicative Differential Equationsmentioning

confidence: 99%

“…In recent years, the orthogonal polynomials have long been used to find the approximate solutions of numerous differential equations in a spectral manner. The popular orthogonal polynomials utilized in MDE solutions are Chebyshev [18], Legendre [19], and Hermite [20]. To the best of our knowledge, there has been no study in the literature that uses Laguerre polynomials in the sense of MDEs solutions.…”

Section: Introductionmentioning

confidence: 99%

“…This is valid for the condition of satisfying (lno f )(t) = ln f (t)[19]. The multiplicative derivative, f * , is treated as the first-order multiplicative derivative.…”

mentioning

confidence: 99%

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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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“…It can be easily demonstrated that the positive and continuous function f(t) on the interval [0, ∞) can be expanded in a series of Laguerre polynomials [19].…”

Section: Multiplicative Differential Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

Kosunalp,

Bas,

Kosunalp

2024

Symmetry

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“…The multiplicative analysis also gives better-thannormal results in many fields, including image processing and artificial intelligence, including computer science, finance, economics, biology, and demography [1][2][3][4][5][6][7][8][9][10]. In recent years, many researchers have conducted various studies on multiplicative analysis and have obtained effective results [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Chebyshev differential equations and multiplicative Chebyshev polynomials

Yalçın

2022

THERM SCI

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In this work, the definition of the first and second types of multiplicative Chebyshev differential equations is given and the solutions of these equations are investigated with the help of multiplicative power series. Also, the properties of first and second type multiplicative Chebyshev polynomials are given and proved. Finally, these studies are supported with numerical examples.

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