Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Sayı: 38, 25 - 33, 31.03.2022
https://doi.org/10.53570/jnt.1060267

Öz

Kaynakça

  • H. M. Srivastava, G. Icoz, B. Cekim, Approximation Properties of an Extended Family of the Szasz-Mirakjan Beta-Type Operator, Axioms 8(111) (2019) 1–13.
  • A. BeLafhal, S. Chib, F. Khannous, T. Usman, Evaluation of Integral Transforms using Special Functions with Applications to Biological Tissues, Computational and Applied Mathematics 40(156) (2021) 1–23.
  • I. Kucukoglu, Y. Simsek, New Formulas and Numbers Arising from Analyzing Combinatorial Numbers and Polynomial, Montes Taurus Journal of Pure and Applied Mathematics 3(3) (2021) 238–259.
  • H. J. Haubold, A. M. Mathai, The Fractional Kinetic Equation and Thermonuclear Functions, Astrophysics and Space Science 273 (2000) 53–63.
  • R. K. Saxena, A. M. Mathai, H. J. Haubold, On Fractional Kinetic Equations, Astrophysics and Space Science 282 (2002) 281–287.
  • R. K. Saxena, A. M. Mathai, H. J. Haubold, On Generalized Fractional Kinetic Equations, Physica A. Statistical Mechanics and its Applications 344 (2004) 657–664.
  • A. Wiman, Uber den Fundamentalsatz in der Theorie der Funktionen E_α (z), Acta Mathematics 29 (1905) 191–201.
  • M. A. Pathan, H. Kumar, On a Logarithmic Mittag-Leffler Function, its Properties and Applications, Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 45(176) (2021) 901–915.
  • T. R. Prabhakar, A Singular Integral Equation with a Generalized Mittag-Leffler Function in the Kernel, Yokohama Mathematical Journal 19 (1971) 7–15.
  • O. Khan, N. Khan, J. Choi, K. S. Nisar, A Type of Fractional Kinetic Equations Associated with the (p,q)-Extended τ-Hypergeometric Functions, Nonlinear Functional Analysis and Application 26(2) (2021) 381–392.
  • R. K. Parmar, On Properties and Applications of (p,q)-Extended τ-Hypergeometric Functions, Comptes Rendus Mathematique 356(3) (2018) 278–282.
  • J. Choi, A. K. Rathie, R. K. Parmar, Extension of Extended Beta, Hypergeometric and Confluent Hypergeometric Functions, Honam Mathematical Journal 36(2) (2014) 339–367.
  • D. L. Suthar, D. Kumar, H. Habenom, Solutions of Fractional Kinetic Equation Associated with the Generalised Multiindex Bessel Function via Laplace-Transform, Differential Equations and Dynamical Systems (2019) 1–14.
  • D. L. Suthar, H. Habenom, K. S. Nisar, Solutions of Fractional Kinetic Equation and the Generalized Galué type Struve Function, Journal of Interdisciplinary Mathematics 22(7) (2019) 1167–1184.
  • H. Habenom, D. L. Suthar, M. Gebeyehu, Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué type Struve Function, Advances in Mathematical Physics Article ID 5074039 (2019) 8 pages.
  • D. L. Suthar, S. D. Purohit, S. Araci, Solution of Fractional Kinetic Equations Associated with the (p, q)-Mathieu-Type Series, Discrete Dynamics in Nature and Society Article ID 8645161 (2020) 7 pages.
  • H. Habenom, A. Oli, D. L. Suthar, (p, q)-Extended Struve Function: Fractional Integrations and Application to Fractional Kinetic Equations, Journal of Mathematics Article ID 5536817 (2021) 1–10.
  • D. L. Suthar, S. D. Purohit, H., Habenom, J. Singh, Class of Integrals and Applications of Fractional Kinetic Equation with the Generalized Multi-Index Bessel Function, Discrete and Continuous Dynamical Systems Series S 14(10) (2021) 3803–3819.
  • D. L. Suthar, S. Chandak, A. Hafte, Unified Fractional Integral and Derivative Formulas, Integral Transforms of Incomplete τ-Hypergeometric Function, Afrika Matematik 32(2020) 599–620.
  • D. L. Suthar, L. N. Mishra, A. M. Khan, A. Alaria, Fractional Integrals for the Product of Srivastava’s Polynomial and (p,q)-Extended Hypergeometric Function, TWMS Journal of Applied and Engineering Mathematics 9(4) (2019) 822–829.
  • U. M. Abubakar, A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators via Modified Extended Beta Function with Applications to Generating Functions, Çankaya University Journal of Science and Engineering (2022) In Press.
  • R. Şahin, O. Yağcı, A New Generalization of Pocchhammer Symbol and Its Applications, Applied Mathematics and Nonlinear Sciences 5(1) (2020) 255–266.
  • A. Mousa, On the Fractional Triple Elzaki Transform and its Properties, Bulletin of Pure and Applied Science Section-E-Mathematics & Statistics 38 E (2) (2019) 641–649.
  • H. M. Srivastava, R. K. Saxena, Operators of Fractional Integral and Their Applications, Applied Mathematics and Computation 118 (2001) 1–52.
  • A. Dahlia, R. Qudsi, Perbandinga Transformasi Laplace dan Transformasi Shehu Untuk Meeny elesaikan Persamaan Integral Volterra, Jenispertama Journal Pendidikan Matematika 5(1) (2021) 1–6.
  • K. B. Kachhia, P. Agarwal, J. C. Prajapati, Certain Image Formulae and Fractional Kinetic Equations Involving Extended Hypergeometric Functions, Advance in Real and Complex Analysis with Applications (2017) 1–32.
  • H. M. Srivastava, H. I. Manocha, A Treatise on Generating Functions. John Wiley & Sons, Chichester, New York, USA, 1984.
  • N. Virchenko, S. L Kalla, A. Al-Zamel, Some Results on a Generalized Hypergeometric Functions, Integral Transforms and Special functions 12(1) (2001) 89–100.
  • N. Virchenko, On the Generalized Confluent Hypergeometric Function and Its Application, Fractional Calculus and Applied Analysis 9(2) (2006) 101–108.
  • M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s Beta Function, Journal of Computation and Applied Mathematics 78 (1997) 19–32.
  • M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended Hypergeometric and Confluent Hypergeometric Functions, Applied Mathematics and Computation 159 (2004) 589–604.

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

Yıl 2022, Sayı: 38, 25 - 33, 31.03.2022
https://doi.org/10.53570/jnt.1060267

Öz

The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function to introduce the $(p,q;l)$-extended $τ$-Gauss hypergeometric and the $(p,q;l)$-extended $τ$-confluent hypergeometric functions with some of their properties, such as the Laplace-type and the Euler-type integral formulas. Another is to apply them to fractional kinetic equations that appear in astrophysics and physics using the Laplace transform method.

Kaynakça

  • H. M. Srivastava, G. Icoz, B. Cekim, Approximation Properties of an Extended Family of the Szasz-Mirakjan Beta-Type Operator, Axioms 8(111) (2019) 1–13.
  • A. BeLafhal, S. Chib, F. Khannous, T. Usman, Evaluation of Integral Transforms using Special Functions with Applications to Biological Tissues, Computational and Applied Mathematics 40(156) (2021) 1–23.
  • I. Kucukoglu, Y. Simsek, New Formulas and Numbers Arising from Analyzing Combinatorial Numbers and Polynomial, Montes Taurus Journal of Pure and Applied Mathematics 3(3) (2021) 238–259.
  • H. J. Haubold, A. M. Mathai, The Fractional Kinetic Equation and Thermonuclear Functions, Astrophysics and Space Science 273 (2000) 53–63.
  • R. K. Saxena, A. M. Mathai, H. J. Haubold, On Fractional Kinetic Equations, Astrophysics and Space Science 282 (2002) 281–287.
  • R. K. Saxena, A. M. Mathai, H. J. Haubold, On Generalized Fractional Kinetic Equations, Physica A. Statistical Mechanics and its Applications 344 (2004) 657–664.
  • A. Wiman, Uber den Fundamentalsatz in der Theorie der Funktionen E_α (z), Acta Mathematics 29 (1905) 191–201.
  • M. A. Pathan, H. Kumar, On a Logarithmic Mittag-Leffler Function, its Properties and Applications, Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 45(176) (2021) 901–915.
  • T. R. Prabhakar, A Singular Integral Equation with a Generalized Mittag-Leffler Function in the Kernel, Yokohama Mathematical Journal 19 (1971) 7–15.
  • O. Khan, N. Khan, J. Choi, K. S. Nisar, A Type of Fractional Kinetic Equations Associated with the (p,q)-Extended τ-Hypergeometric Functions, Nonlinear Functional Analysis and Application 26(2) (2021) 381–392.
  • R. K. Parmar, On Properties and Applications of (p,q)-Extended τ-Hypergeometric Functions, Comptes Rendus Mathematique 356(3) (2018) 278–282.
  • J. Choi, A. K. Rathie, R. K. Parmar, Extension of Extended Beta, Hypergeometric and Confluent Hypergeometric Functions, Honam Mathematical Journal 36(2) (2014) 339–367.
  • D. L. Suthar, D. Kumar, H. Habenom, Solutions of Fractional Kinetic Equation Associated with the Generalised Multiindex Bessel Function via Laplace-Transform, Differential Equations and Dynamical Systems (2019) 1–14.
  • D. L. Suthar, H. Habenom, K. S. Nisar, Solutions of Fractional Kinetic Equation and the Generalized Galué type Struve Function, Journal of Interdisciplinary Mathematics 22(7) (2019) 1167–1184.
  • H. Habenom, D. L. Suthar, M. Gebeyehu, Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué type Struve Function, Advances in Mathematical Physics Article ID 5074039 (2019) 8 pages.
  • D. L. Suthar, S. D. Purohit, S. Araci, Solution of Fractional Kinetic Equations Associated with the (p, q)-Mathieu-Type Series, Discrete Dynamics in Nature and Society Article ID 8645161 (2020) 7 pages.
  • H. Habenom, A. Oli, D. L. Suthar, (p, q)-Extended Struve Function: Fractional Integrations and Application to Fractional Kinetic Equations, Journal of Mathematics Article ID 5536817 (2021) 1–10.
  • D. L. Suthar, S. D. Purohit, H., Habenom, J. Singh, Class of Integrals and Applications of Fractional Kinetic Equation with the Generalized Multi-Index Bessel Function, Discrete and Continuous Dynamical Systems Series S 14(10) (2021) 3803–3819.
  • D. L. Suthar, S. Chandak, A. Hafte, Unified Fractional Integral and Derivative Formulas, Integral Transforms of Incomplete τ-Hypergeometric Function, Afrika Matematik 32(2020) 599–620.
  • D. L. Suthar, L. N. Mishra, A. M. Khan, A. Alaria, Fractional Integrals for the Product of Srivastava’s Polynomial and (p,q)-Extended Hypergeometric Function, TWMS Journal of Applied and Engineering Mathematics 9(4) (2019) 822–829.
  • U. M. Abubakar, A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators via Modified Extended Beta Function with Applications to Generating Functions, Çankaya University Journal of Science and Engineering (2022) In Press.
  • R. Şahin, O. Yağcı, A New Generalization of Pocchhammer Symbol and Its Applications, Applied Mathematics and Nonlinear Sciences 5(1) (2020) 255–266.
  • A. Mousa, On the Fractional Triple Elzaki Transform and its Properties, Bulletin of Pure and Applied Science Section-E-Mathematics & Statistics 38 E (2) (2019) 641–649.
  • H. M. Srivastava, R. K. Saxena, Operators of Fractional Integral and Their Applications, Applied Mathematics and Computation 118 (2001) 1–52.
  • A. Dahlia, R. Qudsi, Perbandinga Transformasi Laplace dan Transformasi Shehu Untuk Meeny elesaikan Persamaan Integral Volterra, Jenispertama Journal Pendidikan Matematika 5(1) (2021) 1–6.
  • K. B. Kachhia, P. Agarwal, J. C. Prajapati, Certain Image Formulae and Fractional Kinetic Equations Involving Extended Hypergeometric Functions, Advance in Real and Complex Analysis with Applications (2017) 1–32.
  • H. M. Srivastava, H. I. Manocha, A Treatise on Generating Functions. John Wiley & Sons, Chichester, New York, USA, 1984.
  • N. Virchenko, S. L Kalla, A. Al-Zamel, Some Results on a Generalized Hypergeometric Functions, Integral Transforms and Special functions 12(1) (2001) 89–100.
  • N. Virchenko, On the Generalized Confluent Hypergeometric Function and Its Application, Fractional Calculus and Applied Analysis 9(2) (2006) 101–108.
  • M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s Beta Function, Journal of Computation and Applied Mathematics 78 (1997) 19–32.
  • M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended Hypergeometric and Confluent Hypergeometric Functions, Applied Mathematics and Computation 159 (2004) 589–604.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Umar Muhammad Abubakar 0000-0003-3935-4829

Yayımlanma Tarihi 31 Mart 2022
Gönderilme Tarihi 19 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 38

Kaynak Göster

APA Abubakar, U. M. (2022). Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function. Journal of New Theory(38), 25-33. https://doi.org/10.53570/jnt.1060267
AMA Abubakar UM. Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function. JNT. Mart 2022;(38):25-33. doi:10.53570/jnt.1060267
Chicago Abubakar, Umar Muhammad. “Solutions of Fractional Kinetic Equations Using the $(p,q;L)$-Extended τ -Gauss Hypergeometric Function”. Journal of New Theory, sy. 38 (Mart 2022): 25-33. https://doi.org/10.53570/jnt.1060267.
EndNote Abubakar UM (01 Mart 2022) Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function. Journal of New Theory 38 25–33.
IEEE U. M. Abubakar, “Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function”, JNT, sy. 38, ss. 25–33, Mart 2022, doi: 10.53570/jnt.1060267.
ISNAD Abubakar, Umar Muhammad. “Solutions of Fractional Kinetic Equations Using the $(p,q;L)$-Extended τ -Gauss Hypergeometric Function”. Journal of New Theory 38 (Mart 2022), 25-33. https://doi.org/10.53570/jnt.1060267.
JAMA Abubakar UM. Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function. JNT. 2022;:25–33.
MLA Abubakar, Umar Muhammad. “Solutions of Fractional Kinetic Equations Using the $(p,q;L)$-Extended τ -Gauss Hypergeometric Function”. Journal of New Theory, sy. 38, 2022, ss. 25-33, doi:10.53570/jnt.1060267.
Vancouver Abubakar UM. Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function. JNT. 2022(38):25-33.


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