Riemann–Liouville fractional operators of bicomplex order and its properties

Goswami, Mahesh Puri; Kumar, Raj

doi:10.1002/mma.8135

Cited by 3 publications

(2 citation statements)

References 46 publications

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“…In [13], there are some important arithmetic properties, let , we have ( 7) and (8) since the orthogonal property of . The strength properties can be concluded naturally.…”

Section: Split Complex Numbermentioning

confidence: 99%

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The Abel Theory of Power Series in Split-Complex Analysis

Cui,

Huang,

Pan

2023

HSET

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The Split-complex number is a generalization of real number , which is a commutative ring with two zero divisors generated by two real numbers. In this paper, we first study the Abel theorem of power series and obtain root and ratio convergent criterion in split-complex analysis. Then this paper shows these regions of convergence by figures in split-complex space. Finally, from our perspective, the results presented in this work represent the extensions of the related ideas or findings in real analysis, which makes it possible to study them in a larger domain.

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“…In [13], there are some important arithmetic properties, let , we have ( 7) and (8) since the orthogonal property of . The strength properties can be concluded naturally.…”

Section: Split Complex Numbermentioning

confidence: 99%

“…In 2015, Emanuello and Nolder [3] studied Möbius geometry on and also considered conformal maps on compactifications and their fundamental properties. For more details, please see earlier studies research [4][5][6][7][8] and so on.…”

Section: Introductionmentioning

confidence: 99%

The Abel Theory of Power Series in Split-Complex Analysis

Cui,

Huang,

Pan

2023

HSET

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Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications

Goswami,

Kumar

2024

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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Extensions of Bicomplex Hypergeometric Functions and Riemann–Liouville Fractional Calculus in Bicomplex Numbers

Bakhet,

Fathi,

Zakarya

et al. 2024

Fractal Fract

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In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral and derivative representations. Furthermore, we delve into the k-Riemann–Liouville fractional integral and derivative within a bicomplex operator, proving several significant theorems. The developed bicomplex hypergeometric functions and bicomplex fractional operators are demonstrated to have practical applications in various fields. This paper also highlights the essential concepts and properties of bicomplex numbers, special functions, and fractional calculus. Our results enhance the overall comprehension and possible applications of bicomplex numbers in mathematical analysis and applied sciences, providing a solid foundation for future research in this field.

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Riemann–Liouville fractional operators of bicomplex order and its properties

Cited by 3 publications

References 46 publications

The Abel Theory of Power Series in Split-Complex Analysis

The Abel Theory of Power Series in Split-Complex Analysis

Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications

Extensions of Bicomplex Hypergeometric Functions and Riemann–Liouville Fractional Calculus in Bicomplex Numbers

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