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Some fractional differential equations involving generalized hypergeometric functions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper, using the generalized Marichev-Saigo-Maeda fractional operator, the authors establish some fractional differential equations associated with generalized hypergeometric functions and, by employing integral transforms, present some image formulas of the resulting equations.
Wydawca
Rocznik
Strony
37--44
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
  • Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India,
autor
  • School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, 300387
  • Institute of Mathematics, Henan Polytechnic University, Jiaozuo, Henan, 454010, P. R. China
autor
  • Department of Mathematics, Baba Farid College, Bathinda, Punjab 151001, India
autor
  • Department of Mathematics, Mata Sahib Kaur Girls College, Talwandi Sabo, Bathinda-151103
  • Research Scholar, Department of Mathematics, Singhania University, Pacheri Bari, Jhunjhunu, India
Bibliografia
  • [1] M. A. Chaudhry, A. Qadir, M. Rafique and S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math. 78 (1997), no. 1, 19-32.
  • [2] M. A. Chaudhry, A. Qadir, H. M. Srivastava and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput. 159 (2004), no. 2, 589-602.
  • [3] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
  • [4] V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Res. Notes Math. Ser. 301, Longman Scientific & Technical, Harlow, 1994.
  • [5] V. Kiryakova, On two Saigo’s fractional integral operators in the class of univalent functions, Fract. Calc. Appl. Anal. 9 (2006), no. 2, 159-176.
  • [6] O. I. Marichev, Volterra equation of Mellin convolution type with a Horn function in the kernel, Izv. AN BSSR Ser. Fiz.-Mat. Nauk 1 (1974), 128-129.
  • [7] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
  • [8] E. Özergin, Some properties of hypergeometric functions, Ph.D. thesis, Eastern Mediterranean University, 2011.
  • [9] E. Özergin, M. A. Özarslan and A. Altın, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235 (2011), no. 16, 4601-4610.
  • [10] R. K. Parmar, A new generalization of gamma, beta, hypergeometric and confluent hypergeometric functions, Matematiche (Catania) 68 (2013), no. 2, 33-52.
  • [11] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of Their Applications, Math. Sci. Eng. 198, Academic Press, San Diego, 1999.
  • [12] T. Pohlen, The Hadamard product and universal power series, Dissertation, Universitat Trier, 2009.
  • [13] E. D. Rainville, Special Functions, first ed., Chelsea, New York, 1971.
  • [14] M. Saigo, On generalized fractional calculus operators: Recent advances in applied mathematics, in: Proceedings of the International Workshop held at Kuwait University (Kuwait 1996), Kuwait University, Kuwait (1996).
  • [15] M. Saigo and A. A. Kilbas, Generalized fractional calculus of the H-function, Fukuoka Univ. Sci. Rep. 29 (1999), no. 1, 31-45.
  • [16] M. Saigo and N. Maeda, More generalization of fractional calculus, in: Transform Methods & Special Functions (Varna ’96), Bulgarian Academy of Sciences, Sofia (1998), 386-400.
  • [17] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science, Yverdon, 1993.
  • [18] R. K. Saxena and M. Saigo, Generalized fractional calculus of the H-function associated with the Appell function F3, J. Fract. Calc. 19 (2001), 89-104.
  • [19] I. N. Sneddon, The Use of Integral Transforms, Tata McGraw-Hill, New Delhi, 1972.
  • [20] H. M. Srivastava and P. Agarwal, Certain fractional integral operators and the generalized incomplete hypergeometric functions, Appl. Appl. Math. 8 (2013), no. 2, 333-345.
  • [21] H. M. Srivastava, R. Agarwal and S. Jain, Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions, Math. Methods Appl. Sci. 40 (2017), no. 1, 255-273.
  • [22] H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 (2014), 484-491.
  • [23] H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Amsterdam, 2012.
  • [24] H. M. Srivastava and M. Saigo, Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation, J. Math. Anal. Appl. 121 (1987), no. 2, 325-369.
  • [25] H. M. Srivastava and V. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput. 211 (2009), no. 1, 198-210.
  • [26] R. Srivastava and N. E. Cho, Some extended Pochhammer symbols and their applications involving generalized hypergeometric polynomials, Appl. Math. Comput. 234 (2014), 277-285.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2a2cee4a-2840-498d-b5d1-1cbc3de1045d
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