Volume 70 | Issue 10 | Year 2024 | Article Id. IJMTT-V70I10P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I10P102
Received | Revised | Accepted | Published |
---|---|---|---|
08 Aug 2024 | 18 Sep 2024 | 07 Oct 2024 | 26 Oct 2024 |
In this paper, researcher develop three theorems by using Marichev – Saigo – Maeda fractional calculus operator, applied the product of the Srivastava polynomial, M – Series and k – Struve function with the help of some lemma. The results are presented in terms of the Generalized k – Wright function. Also obtained some known and intriguing special cases.
MSM fractional integral operator, M-series, k-Struve function.
[1] Rudolf Gorenflo, Yuri Luchko, and Francesco Mainardi, “Analytic Properties and Application of The Wright Function,” Fractional Calculus and Applied Analysis, vol. 2, no. 4, pp. 383-414, 1999.
[CrossRef] [Google Scholar] [Publisher Link]
[2] OI Marichev, “Volterra Equation of Mellin Convolution Type with A Horn Function in The Kernel,” Scienceopen, vol. 1, pp. 128-129, 1974.
[Google Scholar] [Publisher Link]
[3] Kottakkaran Sooppy Nisar, Saiful Rahman Mondal, and Junesang Choi, “Certain Inequalities Involving The K-Struve Function,” Journal of Inequalities and Applications volume, vol. 71, pp. 1-8, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Kottakkaran Sooppy Nisar, Sunil Dutt Purohit, and Saiful. R. Mondal, “Generalized Fractional Kinetic Equations Involving Generalized Struve Function of The First Kind,” Journal of King Saud University-Science, vol. 28, no. 2, pp. 167-171, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Kottakkaran Sooppy Nisar et al., “Some Unified Integral Associated with The Generalized Struve Function,” Proceedings of the Jangjeon Mathematical Society, vol. 20, no. 2, pp. 261-267, 2017.
[Google Scholar] [Publisher Link]
[6] Anatoliĭ Platonovich Prudnikov, I︠ U︡riĭ Aleksandrovich Brychkov, and Oleg Igorevich Marichev, O.I., Integrals and Series, More Special Functions, Gordon and Breach, New York, 1990.
[Google Scholar] [Publisher Link]
[7] A. Erdélyi et al., Higher Transcendental Functions, McGraw-Hill, New York-Toronto-London, 1953.
[Google Scholar] [Publisher Link]
[8] Anatoly A. Kilbas, Megumi Saigo, and Juan J. Trujillo, “On the Generalized Wright Function,” Fractional Calculus and Applied Analysis, vol. 5, no. 4, pp. 437-460, 2002.
[Google Scholar] [Publisher Link]
[9] Kuldeep Singh Gehlot, and Jyotindra C. Prajapati, “On Generalization Of K-Wright Functions and Its Properties,” Pacific Journal of Applied Mathematics, vol. 5, no. 2, pp. 81-88, 2013.
[Google Scholar] [Publisher Link]
[10] Rafael Diaz, and Eddy Pariguan, “On Hypergeometric Functions and Pochammer K-Symbol,” Divulgaciones Mathematics, vol. 15, no. 2, pp. 179-192, 2007.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Megumi Saigo, “A Remark on Integral Operators Involving the Gauss Hypergeometric Functions,” Kyushu University, vol. 11, no. 2, pp. 135-143, 1978.
[CrossRef] [Google Scholar] [Publisher Link]
[12] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science, North Holland, 2006.
[Google Scholar] [Publisher Link]
[13] Saigo, Megumi, and Nobuyuki Maeda, “More Generalization of Fractional Calculus,” Transform Methods and Special Functions, Varna, Bulgaria, pp. 386-400, 1996.
[Google Scholar]
[14] H. M. Srivastava, “On an Extension of The Mittag-Leffler Function, Yokohama Mathematical Journal, vol. 16, no. 2, pp. 77-88, 1968.
[Google Scholar] [Publisher Link]
[15] Vishnu Narayan Mishra, D. L. Suthar, and S. D. Purohit, “Marichev-Saigo-Maeda Fractional Calculus Operator, Srivastava Polynomial and Generalized Mittag-Leffler Function,” Cogent Mathematics, pp. 1-11, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Seema Kabra et al., “The Marichev-Saigo-Meda Fractional Calculus Operator Pertaining to the Generalized k-Struve Function,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 593-602, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Árpád Baricz, Generalized Bessel Functions of The First Kind, Lecture Notes in Mathematics, 1st ed., Springer Berlin, Heidelberg, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[18] K.N Bhowmick, “A Generalized Struve's Function and its Recurrence Formula,” Vijnana Parishad Anusandhan Patrika, vol. 6, pp. 1-11, 1963.
[Google Scholar]
[19] Haile Habenom, D. L. Suthar, and Melaku Gebeyehu, “Application of Laplace Transform on Fractional Kinetic Equation Pertaining to The Generalized Galué Type Struve Function,” Advances in Mathematical Physics, vol. 2019, no. 1, pp. 1-8, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[20] B.N. Kanth, “Integrals Involving Generalized Struve’s Function,” The Nepali Mathematical Sciences Report, vol. 6, no. 1-2, pp. 61-64, 1981.
[Google Scholar]
[21] R.P. Sing, “Some Integral Representation of Generalized Struve’s Function, Math. Ed (Siwan), vol. 22, no. 3, pp. 91-94, 1988.
[Google Scholar]
[22] D.L. Suthar, S.D. Purohit and K.S. Nisar, “Integral Transforms of The Galue Type Struve Function,” TWMS Journal of Applied and Engineering Mathematics, vol. 8, no. 1, pp. 114-121, 2018.
[Google Scholar] [Publisher Link]
[23] Nihat Yagmur, and Halit Orhan, “Starlikeness and Convexity of Generalized Struve Functions,” Abstract and Applied Analysis, vol. 2013, pp1-6, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[24] Manoj Sharma, “Fractional Integration and Fractional Differentiation of the M-Series,” Fractional Calculus and Applied Analysis, vol. 11, no. 2, pp. 187-192, 2008.
[Google Scholar] [Publisher Link]
[25] Hemlata Saxena, and Danishwar Farooq, “The Marichev-Saigo-Maeda Fractional Calculus Operator Associated With The Product Of A General Class Of Polynomial And Generalized Struve Function, International Journal of Difference Equations (IJDE), vol. 18, no.1, pp. 299-307, 2023.
[Publisher Link]
Danishwar Farooq, Hemlata Saxena, "The Marichev – Saigo – Maeda Fractional Calculus Operator Associated with the Product of a General Class of Polynomial, M – Series and Generalized k – Struve Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 10, pp. 7-13, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I10P102