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Journals / Cankaya University Journal of Science and Engineering / 2022 / Cilt: 19 - Sayı: 1

A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions

Umar Muhammad ABUBAKAR
Pages
40–50
Publication Date
2022-05-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The Mellin of certain new extension of the extended fractional derivative and integral operators ware obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article object is to introduce new extension of the extended beta, Gauss hypergeometric, Appell hypergeometric and Lauricella hypergeometric functions.
📊
Key Findings & Data:The new extension of the extended Riemann-Liouville, Caputo and Kober-Erdelyi fractional derivative and integral operators are also examined with their applications to generating functions by considering the extended hypergeometric functions.
💡
Conclusion & Impact:The Mellin of certain new extension of the extended fractional derivative and integral operators ware obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Beta function · Fractional calculus · Gamma function

Abstract

This article object is to introduce new extension of the extended beta, Gauss hypergeometric, Appell hypergeometric and Lauricella hypergeometric functions. The new extension of the extended Riemann-Liouville, Caputo and Kober-Erdelyi fractional derivative and integral operators are also examined with their applications to generating functions by considering the extended hypergeometric functions. The Mellin of certain new extension of the extended fractional derivative and integral operators ware obtained.

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Cite This Article

ABUBAKAR, U. M. (2022). A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions. Cankaya University Journal of Science and Engineering, Cilt: 19 - Sayı: 1, 40–50. https://ajindex.com/articles/745970

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References (5)

  1. M. Saif, F. Khan, K.S. Nisar, and S. Araci, “Modified Laplace transform and its properties,” Journal of Mathematics and its Computer Science, vol. 21, pp. 127-135, 2020. A. Gaur, and G. Agarwal, “A new technique to find Laplace transform,” Advances and Applications in Mathematical Sciences, vol. 20, no. 7, pp. 1279-1286, 2021. A. Gaur, and G. Agarwal, “Application of 𝛽 −Laplace integral transform,” Talant Development and Excellent, vol. 12, no. 3s, pp. 1058-1068, 2020. A. Gaur and G. Agarwal, “On 𝛽 −Laplace integral transforms and their properties,” International Journal of Advanced Science and Technology, vol. 29, no. 3s, pp. 1481-1491, 2020. A. Gaur, and G. Agarwal, “Relation of 𝛽 −Laplace integral transforms with other integral transforms,” Test Engineering and Management, vol. 83, pp. 8653-8659, 2020.
  2. A. Gaur, G. Agarwal, K.S. Nisar and A.S. Abusytian “On some properties of 𝛽 −Laplace integral transform,” Journal of Mathematics and Computer Science, vol. 23, pp. 315-320, 2021. A. Gaur, and G. Agarwal, “Some new applications of 𝛽 −Laplace integral transform,” presented at IOP Conference Series: Material Science and Engineering, vol. 1166, Coimbatore, India, 2021. A. Gaur, and G. Agarwal, ‘’Fractional order 𝛽 −Laplace integral transform,’’ Journal of Physics: Conference Series, vol. 1706, 2020.
  3. M. A. Kulip, A. A. Algonah, and S. S. Barahmah, “Modified forms of some classical special functions,” Journal of Mathematical Analysis and Modeling, vol. 1, no. 1, pp. 87-98, 2021. S. S. Barahmah, “Further modified forms of etended beta function and their properties,” Journal of Mathematical Problems, Equations and Statistics, vol. 2, no. 2, pp. 33-42, 2021.
  4. A. Cetinkaya, I. O. Kıymaz, P. Agarwal, and R. P. Agarwal, “A comparative study on generating function relations for generalized hypergeometric functions via generalized fractionnal operators,” Advances in Difference Equations, vol. 156, pp. 1-11, 2018. P. I. Pucheta, “A new extended beta function,” International Journal of Mathematics and Its Applications, vol. 5, no. 3-C, pp. 255-260, 2017. P. I. Pucheta, “The new Riemann-Liouville fractional operator extended,” International Journal of Mathematics and Its Applications, vol. 5, no. 4-D, pp. 491-497, 2017.
  5. U. M. Abubakar, S. R. Kabara, M. A. Lawan, and F. A. Idris, “A new extension of modified gamma and beta functions,” Cankaya University Journal of Science and Engineering, vol. 18, no. 1, pp. 9-23, 2021. U. M. Abubakar, “Applications of the generalized exten