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Yıl 2021, Cilt: 70 Sayı: 2, 678 - 689, 31.12.2021
https://doi.org/10.31801/cfsuasmas.797257

Öz

Kaynakça

  • Agarwal, G., Nisar, K. S., Certain fractional kinetic equations involving generalized K-functions, Analysis, 39(2) (2019), 65-70. https://doi.org/10.1515/anly-2019-0013
  • Agarwal, P., Chand, M., Singh, G., Certain fractional kinetic equations involving the product of generalized k-Bessel function, Alexandria Engineering Journal, 55(4) (2016), 3053-3059. https://doi.org/10.1016/j.aej.2016.07.025
  • Agarwal, P., Ntouyas, S. K., Jain, S., Chand, M., Singh, G., Fractional kinetic equations involving generalized k-Bessel function via Sumudu transform, Alexandria Engineering Journal, 57(3) (2018), 1937-1942. https://doi.org/10.1016/j.aej.2017.03.046
  • Asiru, M. A., Sumudu transform and the solution of integral equation of convolution type, Int. J. Math. Educ. Sci. Technol., 32 (2001), 906-910. https://doi.org/10.1080/002073901317147870
  • Baleanu, D., Khan, O., Khan, N., Nisar, K. S., Computable solution of fractional kinetic equations using Mathieu-type series, Advances in Difference Equations, 2019(1) (2019), 1-13. https://doi.org/10.1186/s13662-019-2167-4
  • Barnes E. W., The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London. Ser. A, 206 (1906), 249-297.
  • Belgacem, F. B. M., Introducing and analyzing deeper Sumudu properties, Nonlinear Stud., 13 (2006), 23-42.
  • Belgacem, F. B. M., Sumudu applications to Maxwells equations, PIERS Online, 5 (2009), 355-360. https://doi.org/10.2529/PIERS090120050621
  • Belgacem, F. B. M., Applications with the Sumudu transform to Bessel functions and equations, Appl. Math. Sci., 4 (2010), 3665-3686.
  • Belgacem, F. B. M., Al-Shemas, E. H., Silambarasan, R., Sumudu computation of the transient magnetic field in a lossy medium, Appl. Math. Inf. Sci., 6 (2016), 1-9.
  • Belgacem, F. B. M., Karaballi, A. A., Sumudu transform fundamental properties investigations and applications, J. Appl. Math. Stoch. Anal., 2006 (2006), 1-23.
  • Belgacem, F. B. M., Karaballi, A. A., Kalla, S. L., Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Probl. Eng., 3 (2003), 103-118.
  • Choi, J., Jang, D. S., Srivastava, H. M., A generalization of the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 19 (2008), 65-79. https://doi.org/10.1080/10652460701528909
  • Choi, J., Parmar, R. K., An extension of the generalized Hurwitz-Lerch Zeta function of two variables, Filomat, 31 (2017), 91-96. https://doi.org/10.2298/FIL1701091C
  • Choi, J., ¸Sahin, R., Yagcı, O., Kim, D., Note on the Hurwitz-Lerch Zeta function of two variables, Symmetry, 12(9) (2020), 1431. https://doi.org/10.3390/sym12091431
  • Chouhan, A., Sarswat, S., On solution of generalized Kinetic equation of fractional order, Int. Jr. of Mathematical Sciences and Applications, 2(2) (2012), 813-818.
  • Chouhan, A., Purohit, S. D., Sarswat, S., An alternative method for solving generalized differential equations of fractional order, Kragujevac J Math, 37 (2013), 299-306.
  • Daman, O., Pathan, M. A., A further generalization of the Hurwitz Zeta function, Math. Sci. Res. J., 16(10) (2012), 251-259.
  • Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953. https://doi.org/10.1002/zamm.19540341220
  • Garg, M., Jain, K., Kalla, S. L., A further study of general Hurwitz-Lerch zeta function, Algebras Groups Geom., 25 (2008), 311-319.
  • Goyal, S. P., Laddha, R. K., On the generalized Zeta function and the generalized Lambert function, Ganita Sandesh, 11 (1997), 99-108.
  • Gupta, P. L., Gupta, R. C., Ong, S.-H., Srivastava, H. M., A class of Hurwitz-Lerch Zeta distributions and their applications in reliability, Appl. Math. Comput., 196 (2008), 521-531. https://doi.org/10.1016/j.amc.2007.06.012
  • Haubold, H. J., Mathai, A. M., The fractional kinetic equation and thermonuclear functions, Astrophys. Space Sci., 327 (2000), 53-63. https://doi.org/10.1023/A:1002695807970
  • Kumar, D., Choi, J., Srivastava, H. M., Solution of a general family of fractional kinetic equations associated with the generalized Mittag-Le­ffler function, Nonlinear Funct. Anal. Appl, 23(3) (2018), 455-471.
  • Lin, S. D., Srivastava, H. M., Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput., 154 (2004), 725-733. https://doi.org/10.1016/S0096-3003(03)00746-X
  • Lin, S. D., Srivastava, H. M., Wang, P. Y., Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions, Integral Transforms Spec. Funct., 17 (2006), 817-822. https://doi.org/10.1080/10652460600926923
  • Mittag-Leffler, G. M., Sur la representation analytique d'une branche uniforme d'une fonction monogene, Acta. Math., 29 (1905), 101-181. https://doi.org/10.1007/BF02403200
  • Nisar, K. S., Shaikh, A., Rahman, G., Kumar, D., Solution of fractional kinetic equations involving class of functions and Sumudu transform, Advances in Difference Equations, 2020(1) (2020), 1-11. https://doi.org/10.1186/s13662-020-2513-6
  • Nisar, K. S., Generalized Mittag-Le­ffler Type Function: Fractional Integrations and Application to Fractional Kinetic Equations, Frontiers in Physics, 8 (2020), 33. https://doi.org/10.3389/fphy.2020.00033
  • Saxena, R. K., Kalla, S. L., On the solutions of certain fractional kinetic equations, Applied Mathematics and Computation, 199(2) (2008), 504-511. https://doi.org/10.1016/j.amc.2007.10.005
  • Saxena, R. K., Mathai, A. M., Haubold, H. J., On fractional kinetic equations, Astrophysics and Space Science, 282(1) (2002), 281-287. https://doi.org/10.1023/A:1021175108964
  • Saxena, R. K., Mathai, A. M., Haubold, H. J., On generalized fractional kinetic equations, Physica A: Statistical Mechanics and its Applications, 344(3-4) (2004), 657-664. https://doi.org/10.1016/j.physa.2004.06.048
  • Srivastava, H. M., A new family of the λ-generalized Hurwitz-Lerch Zeta functions with applications, Appl. Math. Inform. Sci., 8 (2014), 1485-1500. https://doi.org/10.12785/amis/080402
  • Srivastava, H. M., Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Acedemic Publishers, Dordrecht, Boston and London, 2001.
  • Srivastava, H. M., Choi, J., Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  • Srivastava, H. M., Jankov, D., Pogány, T. K., Saxena, R. K., Two-sided inequalities for the extended Hurwitz-Lerch Zeta function, Comput. Math. Appl., 62 (2011), 516-522. https://doi.org/10.1016/j.camwa.2011.05.035
  • Srivastava, H. M., Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  • Srivastava, H. M., Luo, M. J., Raina, R. K., New results involving a class of generalized Hurwitz-Lerch Zeta functions and their applications, Turkish J. Anal. Number Theory, 1 (2013), 26-35.
  • Srivastava, H. M., Manocha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
  • Srivastava, H. M., Saxena, R. K., Operators of fractional integration and their applications, Applied Mathematics and Computation, 118(1) (2001), 1-52. https://doi.org/10.1016/S0096- 3003(99)00208-8
  • Srivastava, H. M., Saxena, R. K., Pogány, T. K., Saxena, R., Integral and computational representations of the extended Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 22 (2011), 487-506. https://doi.org/10.1080/10652469.2010.530128
  • Srivastava, H. M., ¸Sahin, R., Yagcı, O., A family of incomplete Hurwitz-Lerch zeta functions of two variable, Miskolc Mathematical Notes, 21(1) (2020), 401-415. https://doi.org/10.18514/MMN.2020.3058
  • Sahin, R., Yagcı, O., Fractional calculus of the extended hypergeometric function, Applied Mathematics and Nonlinear Sciences, 5(1) (2020), 369-384. https://doi.org/10.2478/amns.2020.1.00035
  • Watugala, G. K., Sumudu Transform-an integral transform to solve differential equations and control engineering problems, Inter.J. Math. Ed. Sci. Tech., 24 (1993), 35-42. https://doi.org/10.1080/0020739930240105
  • Watugala, G. K., Sumudu Transform-a new integral transform to solve differential equations and control engineering problems, Mathematical Engineering in Industry, 6(4) (1998), 319- 329.

Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform

Yıl 2021, Cilt: 70 Sayı: 2, 678 - 689, 31.12.2021
https://doi.org/10.31801/cfsuasmas.797257

Öz

Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.

Kaynakça

  • Agarwal, G., Nisar, K. S., Certain fractional kinetic equations involving generalized K-functions, Analysis, 39(2) (2019), 65-70. https://doi.org/10.1515/anly-2019-0013
  • Agarwal, P., Chand, M., Singh, G., Certain fractional kinetic equations involving the product of generalized k-Bessel function, Alexandria Engineering Journal, 55(4) (2016), 3053-3059. https://doi.org/10.1016/j.aej.2016.07.025
  • Agarwal, P., Ntouyas, S. K., Jain, S., Chand, M., Singh, G., Fractional kinetic equations involving generalized k-Bessel function via Sumudu transform, Alexandria Engineering Journal, 57(3) (2018), 1937-1942. https://doi.org/10.1016/j.aej.2017.03.046
  • Asiru, M. A., Sumudu transform and the solution of integral equation of convolution type, Int. J. Math. Educ. Sci. Technol., 32 (2001), 906-910. https://doi.org/10.1080/002073901317147870
  • Baleanu, D., Khan, O., Khan, N., Nisar, K. S., Computable solution of fractional kinetic equations using Mathieu-type series, Advances in Difference Equations, 2019(1) (2019), 1-13. https://doi.org/10.1186/s13662-019-2167-4
  • Barnes E. W., The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London. Ser. A, 206 (1906), 249-297.
  • Belgacem, F. B. M., Introducing and analyzing deeper Sumudu properties, Nonlinear Stud., 13 (2006), 23-42.
  • Belgacem, F. B. M., Sumudu applications to Maxwells equations, PIERS Online, 5 (2009), 355-360. https://doi.org/10.2529/PIERS090120050621
  • Belgacem, F. B. M., Applications with the Sumudu transform to Bessel functions and equations, Appl. Math. Sci., 4 (2010), 3665-3686.
  • Belgacem, F. B. M., Al-Shemas, E. H., Silambarasan, R., Sumudu computation of the transient magnetic field in a lossy medium, Appl. Math. Inf. Sci., 6 (2016), 1-9.
  • Belgacem, F. B. M., Karaballi, A. A., Sumudu transform fundamental properties investigations and applications, J. Appl. Math. Stoch. Anal., 2006 (2006), 1-23.
  • Belgacem, F. B. M., Karaballi, A. A., Kalla, S. L., Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Probl. Eng., 3 (2003), 103-118.
  • Choi, J., Jang, D. S., Srivastava, H. M., A generalization of the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 19 (2008), 65-79. https://doi.org/10.1080/10652460701528909
  • Choi, J., Parmar, R. K., An extension of the generalized Hurwitz-Lerch Zeta function of two variables, Filomat, 31 (2017), 91-96. https://doi.org/10.2298/FIL1701091C
  • Choi, J., ¸Sahin, R., Yagcı, O., Kim, D., Note on the Hurwitz-Lerch Zeta function of two variables, Symmetry, 12(9) (2020), 1431. https://doi.org/10.3390/sym12091431
  • Chouhan, A., Sarswat, S., On solution of generalized Kinetic equation of fractional order, Int. Jr. of Mathematical Sciences and Applications, 2(2) (2012), 813-818.
  • Chouhan, A., Purohit, S. D., Sarswat, S., An alternative method for solving generalized differential equations of fractional order, Kragujevac J Math, 37 (2013), 299-306.
  • Daman, O., Pathan, M. A., A further generalization of the Hurwitz Zeta function, Math. Sci. Res. J., 16(10) (2012), 251-259.
  • Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953. https://doi.org/10.1002/zamm.19540341220
  • Garg, M., Jain, K., Kalla, S. L., A further study of general Hurwitz-Lerch zeta function, Algebras Groups Geom., 25 (2008), 311-319.
  • Goyal, S. P., Laddha, R. K., On the generalized Zeta function and the generalized Lambert function, Ganita Sandesh, 11 (1997), 99-108.
  • Gupta, P. L., Gupta, R. C., Ong, S.-H., Srivastava, H. M., A class of Hurwitz-Lerch Zeta distributions and their applications in reliability, Appl. Math. Comput., 196 (2008), 521-531. https://doi.org/10.1016/j.amc.2007.06.012
  • Haubold, H. J., Mathai, A. M., The fractional kinetic equation and thermonuclear functions, Astrophys. Space Sci., 327 (2000), 53-63. https://doi.org/10.1023/A:1002695807970
  • Kumar, D., Choi, J., Srivastava, H. M., Solution of a general family of fractional kinetic equations associated with the generalized Mittag-Le­ffler function, Nonlinear Funct. Anal. Appl, 23(3) (2018), 455-471.
  • Lin, S. D., Srivastava, H. M., Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput., 154 (2004), 725-733. https://doi.org/10.1016/S0096-3003(03)00746-X
  • Lin, S. D., Srivastava, H. M., Wang, P. Y., Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions, Integral Transforms Spec. Funct., 17 (2006), 817-822. https://doi.org/10.1080/10652460600926923
  • Mittag-Leffler, G. M., Sur la representation analytique d'une branche uniforme d'une fonction monogene, Acta. Math., 29 (1905), 101-181. https://doi.org/10.1007/BF02403200
  • Nisar, K. S., Shaikh, A., Rahman, G., Kumar, D., Solution of fractional kinetic equations involving class of functions and Sumudu transform, Advances in Difference Equations, 2020(1) (2020), 1-11. https://doi.org/10.1186/s13662-020-2513-6
  • Nisar, K. S., Generalized Mittag-Le­ffler Type Function: Fractional Integrations and Application to Fractional Kinetic Equations, Frontiers in Physics, 8 (2020), 33. https://doi.org/10.3389/fphy.2020.00033
  • Saxena, R. K., Kalla, S. L., On the solutions of certain fractional kinetic equations, Applied Mathematics and Computation, 199(2) (2008), 504-511. https://doi.org/10.1016/j.amc.2007.10.005
  • Saxena, R. K., Mathai, A. M., Haubold, H. J., On fractional kinetic equations, Astrophysics and Space Science, 282(1) (2002), 281-287. https://doi.org/10.1023/A:1021175108964
  • Saxena, R. K., Mathai, A. M., Haubold, H. J., On generalized fractional kinetic equations, Physica A: Statistical Mechanics and its Applications, 344(3-4) (2004), 657-664. https://doi.org/10.1016/j.physa.2004.06.048
  • Srivastava, H. M., A new family of the λ-generalized Hurwitz-Lerch Zeta functions with applications, Appl. Math. Inform. Sci., 8 (2014), 1485-1500. https://doi.org/10.12785/amis/080402
  • Srivastava, H. M., Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Acedemic Publishers, Dordrecht, Boston and London, 2001.
  • Srivastava, H. M., Choi, J., Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  • Srivastava, H. M., Jankov, D., Pogány, T. K., Saxena, R. K., Two-sided inequalities for the extended Hurwitz-Lerch Zeta function, Comput. Math. Appl., 62 (2011), 516-522. https://doi.org/10.1016/j.camwa.2011.05.035
  • Srivastava, H. M., Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  • Srivastava, H. M., Luo, M. J., Raina, R. K., New results involving a class of generalized Hurwitz-Lerch Zeta functions and their applications, Turkish J. Anal. Number Theory, 1 (2013), 26-35.
  • Srivastava, H. M., Manocha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
  • Srivastava, H. M., Saxena, R. K., Operators of fractional integration and their applications, Applied Mathematics and Computation, 118(1) (2001), 1-52. https://doi.org/10.1016/S0096- 3003(99)00208-8
  • Srivastava, H. M., Saxena, R. K., Pogány, T. K., Saxena, R., Integral and computational representations of the extended Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 22 (2011), 487-506. https://doi.org/10.1080/10652469.2010.530128
  • Srivastava, H. M., ¸Sahin, R., Yagcı, O., A family of incomplete Hurwitz-Lerch zeta functions of two variable, Miskolc Mathematical Notes, 21(1) (2020), 401-415. https://doi.org/10.18514/MMN.2020.3058
  • Sahin, R., Yagcı, O., Fractional calculus of the extended hypergeometric function, Applied Mathematics and Nonlinear Sciences, 5(1) (2020), 369-384. https://doi.org/10.2478/amns.2020.1.00035
  • Watugala, G. K., Sumudu Transform-an integral transform to solve differential equations and control engineering problems, Inter.J. Math. Ed. Sci. Tech., 24 (1993), 35-42. https://doi.org/10.1080/0020739930240105
  • Watugala, G. K., Sumudu Transform-a new integral transform to solve differential equations and control engineering problems, Mathematical Engineering in Industry, 6(4) (1998), 319- 329.
Toplam 45 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Oğuz Yağcı 0000-0001-9902-8094

Recep Şahin 0000-0001-5713-3830

Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 19 Eylül 2020
Kabul Tarihi 11 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

APA Yağcı, O., & Şahin, R. (2021). Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 678-689. https://doi.org/10.31801/cfsuasmas.797257
AMA Yağcı O, Şahin R. Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2021;70(2):678-689. doi:10.31801/cfsuasmas.797257
Chicago Yağcı, Oğuz, ve Recep Şahin. “Solution of Fractional Kinetic Equations Involving Generalized Hurwitz-Lerch Zeta Function Using Sumudu Transform”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 2 (Aralık 2021): 678-89. https://doi.org/10.31801/cfsuasmas.797257.
EndNote Yağcı O, Şahin R (01 Aralık 2021) Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 678–689.
IEEE O. Yağcı ve R. Şahin, “Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 2, ss. 678–689, 2021, doi: 10.31801/cfsuasmas.797257.
ISNAD Yağcı, Oğuz - Şahin, Recep. “Solution of Fractional Kinetic Equations Involving Generalized Hurwitz-Lerch Zeta Function Using Sumudu Transform”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (Aralık 2021), 678-689. https://doi.org/10.31801/cfsuasmas.797257.
JAMA Yağcı O, Şahin R. Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:678–689.
MLA Yağcı, Oğuz ve Recep Şahin. “Solution of Fractional Kinetic Equations Involving Generalized Hurwitz-Lerch Zeta Function Using Sumudu Transform”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 2, 2021, ss. 678-89, doi:10.31801/cfsuasmas.797257.
Vancouver Yağcı O, Şahin R. Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):678-89.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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