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Year 2022, Volume: 19 Issue: 1, 40 - 50, 01.05.2022

Umar Muhammad Abubakar

Abstract

References

  • 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.
  • 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.
  • 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. 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.
  • 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 extended mathematical physics functions to the modified Riemann-Liouville fractional derivative operator,” presented at 1st International Conference of Physics, Ankara, Turkey, 2021.
  • U. M. Abubakar, “Applications of the modified extended special functions to statistical distribution and fractional calculus,” presented at Euro Asia 9th. International Congress on Applied Sciences, Erzurum, Turkey, 2021.
  • U. M. Abubakar, “Application of modified extended special function to statistical distribution and fractional calculus,” presented at 30th of August Symposium on Scientific Research, Ankara, Turkey, 2021.
  • R. Şahin, O. Yağcı, M. B. Yağbasan, I. O. Kıymaz, and A. Cetinkaya, “Further generalization of gamma and beta and related functions,” Journal of Inequalities and Special Functions, vol. 9, no. 4, pp. 1-7, 2018.
  • J. Choi, A. K. Rathie, and R. K. Parmar, “Extension of extended beta, hypergeometric and confluent hypergeometric functions,” Honam Mathematical Journal, vol. 36, no. 2, pp. 357-385, 2014.
  • D. Baleanu, P. Agarwal, R. K. Parmar, M. M. Alquarashi, and S. Salahshour, “Extension of the fractional derivative of the Riemann-Liouville,” Journal of Nonlinear Science and Applications, vol. 10, pp. 2914-2924, 2017.
  • M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, “Extension of Euler’s beta function,” Journal of Computational and Applied Mathematics, vol. 78, no. 1, pp. 19-32, 1997.
  • M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, “Extended hypergeometric and confluent hypergeometric functions,” Applied Mathematics and Computation, vol. 159, pp. 589-604, 2004.
  • M. A. Özarslan, and E. Özergin, “Some generating relations for extended hypergeometric functions via generalized fractional derivative operator,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1825-1833, 2010.
  • I. O. Kıymaz, A. Cetinkaya, and P. Agarwal, “An extension of Caputo fractional derivative operator and its applications,” Journal of Nonlinear Science and Applications, vol. 9, pp. 3611-3621, 2016.
  • U. M. Abubakar, “New generalized beta function associated with the Fox-Wright function,” Journal of Fractional Calculus and Application, vol. 12, no. 2, pp. 204-227, 2021.
  • U. M. Abubakar, “A study of extended beta and associated functions connected to Fox-Wright function,” presented at 12th Symposium of the Fractional Calculus and Applications Group, Alexandria, Egypt, 2021.
  • U. M. Abubakar, and S. Patel, “On a new generalized beta function defined by the generalized Wright function and its applications,” Malaysian Journal of Computing, vol. 6, no. 2, pp. 851-870, 2021

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

Year 2022, Volume: 19 Issue: 1, 40 - 50, 01.05.2022

Umar Muhammad Abubakar

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.

Keywords

Beta function Fractional calculus Gamma function Mellin transform.

References

  • 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.
  • 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.
  • 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. 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.
  • 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 extended mathematical physics functions to the modified Riemann-Liouville fractional derivative operator,” presented at 1st International Conference of Physics, Ankara, Turkey, 2021.
  • U. M. Abubakar, “Applications of the modified extended special functions to statistical distribution and fractional calculus,” presented at Euro Asia 9th. International Congress on Applied Sciences, Erzurum, Turkey, 2021.
  • U. M. Abubakar, “Application of modified extended special function to statistical distribution and fractional calculus,” presented at 30th of August Symposium on Scientific Research, Ankara, Turkey, 2021.
  • R. Şahin, O. Yağcı, M. B. Yağbasan, I. O. Kıymaz, and A. Cetinkaya, “Further generalization of gamma and beta and related functions,” Journal of Inequalities and Special Functions, vol. 9, no. 4, pp. 1-7, 2018.
  • J. Choi, A. K. Rathie, and R. K. Parmar, “Extension of extended beta, hypergeometric and confluent hypergeometric functions,” Honam Mathematical Journal, vol. 36, no. 2, pp. 357-385, 2014.
  • D. Baleanu, P. Agarwal, R. K. Parmar, M. M. Alquarashi, and S. Salahshour, “Extension of the fractional derivative of the Riemann-Liouville,” Journal of Nonlinear Science and Applications, vol. 10, pp. 2914-2924, 2017.
  • M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, “Extension of Euler’s beta function,” Journal of Computational and Applied Mathematics, vol. 78, no. 1, pp. 19-32, 1997.
  • M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, “Extended hypergeometric and confluent hypergeometric functions,” Applied Mathematics and Computation, vol. 159, pp. 589-604, 2004.
  • M. A. Özarslan, and E. Özergin, “Some generating relations for extended hypergeometric functions via generalized fractional derivative operator,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1825-1833, 2010.
  • I. O. Kıymaz, A. Cetinkaya, and P. Agarwal, “An extension of Caputo fractional derivative operator and its applications,” Journal of Nonlinear Science and Applications, vol. 9, pp. 3611-3621, 2016.
  • U. M. Abubakar, “New generalized beta function associated with the Fox-Wright function,” Journal of Fractional Calculus and Application, vol. 12, no. 2, pp. 204-227, 2021.
  • U. M. Abubakar, “A study of extended beta and associated functions connected to Fox-Wright function,” presented at 12th Symposium of the Fractional Calculus and Applications Group, Alexandria, Egypt, 2021.
  • U. M. Abubakar, and S. Patel, “On a new generalized beta function defined by the generalized Wright function and its applications,” Malaysian Journal of Computing, vol. 6, no. 2, pp. 851-870, 2021
There are 26 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Umar Muhammad Abubakar 0000-0003-3935-4829

Publication Date May 1, 2022
Published in Issue Year 2022 Volume: 19 Issue: 1

Cite

APA 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, 19(1), 40-50.
AMA Abubakar UM. A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions. CUJSE. May 2022;19(1):40-50.
Chicago Abubakar, Umar Muhammad. “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 19, no. 1 (May 2022): 40-50.
EndNote Abubakar UM (May 1, 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 19 1 40–50.
IEEE U. M. Abubakar, “A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions”, CUJSE, vol. 19, no. 1, pp. 40–50, 2022.
ISNAD Abubakar, Umar Muhammad. “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 19/1 (May 2022), 40-50.
JAMA Abubakar UM. A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions. CUJSE. 2022;19:40–50.
MLA Abubakar, Umar Muhammad. “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, vol. 19, no. 1, 2022, pp. 40-50.
Vancouver Abubakar UM. A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions. CUJSE. 2022;19(1):40-5.