Neki integrali koji uključuju generalizovane Mitag-Leflerove funkcije
Sažetak
Uvod/cilj: Definisani su neki integrali koji uključuju generalizovanu Mitag-Leflerovu funkciju sa različitim vrstama polinoma.
Metode: Svojstva generalizovane Mitag-Leflerove funkcije koriste se na različitim vrstama polinoma, kao što su Jakobijevi, Ležandrovi, Ermitovi, kako bi odredili njihove integrale.
Rezultati: Izvedene su neke integralne formule koje uključuju Ležandrovu funkciju, Besel-Mejtlandovu funkciju i generalizovane hipergeometrijske funkcije.
Zaključak: Dobijeni rezultati su opšte prirode i mogli bi biti korisni za utvrđivanje drugih integralnih formula koje uključuju druge vrste polinoma.
Reference
Dorrego, G.A. & Cerutti R.A. 2012. The k-Mittag-Leffler function. International Journal of Contemporary Mathematics Sciences, 7(15), pp.705-716 [online]. Available at: http://www.m-hikari.com/ijcms/ijcms-2012/13-16-2012/ceruttiIJCMS13-16-2012-2.pdf [Accessed: 20 August 2022].
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F.G. 1953a. Higher transcendental functions Volume 1 (Bateman Manuscript Project) [online]. New York, Toronto and London: McGraw-Hill Book Company. Available at: https://authors.library.caltech.edu/43491/19/Volume%201.pdf [Accessed: 20 August 2022].
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F.G. 1953b. Higher transcendental functions Volume 3 (Bateman Manuscript Project) [online]. New York, Toronto and London: McGraw-Hill Book Company. Available at: https://authors.library.caltech.edu/43491/10/Volume%203.pdf [Accessed: 20 August 2022].
Faraj, A.W., Salim, T.O., Sadek, S. & Ismail, J. 2013. Generalized Mittag-effler Function Associated with Weyl Fractional Calculus Operators. Journal of Mathematics, 2013(art ID:821762). Available at: https://doi.org/10.1155/2013/821762
Gehlot, K.S. 2021. The generalized k-Mittag-Leffler function. International Journal of Contemporary Mathematical Sciences, 7, pp.2213-2219.
Haq, S., Khan, A.H. & Nisar, K.S. 2019. A study of new class of integrals associated with generalized Struve function and polynomials. Communications of the Korean Mathematical Society, 34(1), pp.169-183. Available at: https://doi.org/10.4134/CKMS.c170490
Khan, M.A. & Ahmed, S. 2012. Fractional calculus operators involving generalized Mittag-Leffler function. World Applied Programming, 2(12), pp.492-499.
McBride, A.C. 1995. V. Kiryakova Generalized fractional calculus and applications (Pitman Research Notes in Mathematics Vol. 301, Longman1994), 388 pp., 0 582 21977 9, £39. Proceedings of the Edinburgh Mathematical Society, 38(1), pp.189-190. Available at: https://doi.org/10.1017/S0013091500006325
Mittag-Leffler, G.M. 1903. Sur la nouvelle fonction Eα(x). CR Acad. Sci. Paris, 137(2), pp.554-558.
Nadir, A., Khan, A. & Kalim, M. 2014. Integral transforms of the generalized Mittag-Leffler function. Applied Mathematical Science, 8(103), pp.5145-5154. Available at: https://doi.org/10.12988/ams.2014.43218
Prabhakar, T.R. 1971. A singular integral equation with a generalized Mittag Leffler function in the kernel. Yokohama Mathematical Journal, 19(1), pp.7-15 [online]. Available at: https://ynu.repo.nii.ac.jp/?action=pages_view_main&active_action=repository_view_main_item_detail&item_id=6514&item_no=1&page_id=15&block_id=22 [Accessed: 20 August 2022].
Prajapati, J.C., Jana, R.K., Saxena, R.K. & Shukla, A.K. 2013. Some results on the generalized Mittag-Leffler function operator. Journal of Inequalities and Applications, 2013(art.number:33). Available at: https://doi.org/10.1186/1029-242X-2013-33
Prajapati, J.C. & Shukla, A.K., 2012. Decomposition of Generalized Mittag-Leffler Function and Its Properties. Advances in Pure Mathematics, 2(1), p.8-14. Available at: https://doi.org//10.4236/apm.2012.21003
Purohit, S.D., Kalla, S.L. & Suthar, D.L. 2011. Fractional integral operators and the multiindex Mittag-Leffler functions. SCIENTIA Series A: Mathematical Sciences, 21, pp.87–96 [online]. Available at: http://scientia.mat.utfsm.cl/archivos/vol21/vol21art9.pdf [Accessed: 20 August 2022].
Rainville, E.D. 1960. Special functions (Vol. 5). New York: The Macmillan Company.
Salim, T.O. & Faraj, A.W. 2012. A generalization of Mittag-Leffler function and integral operator associated with fractional calculus. Journal of Fractional Calculus and Applications, 3(5), pp.1-13 [online]. Available at: https://www.naturalspublishing.com/download.asp?ArtcID=1893 [Accessed: 20 August 2022].
Saxena, V.P. 2008. The I-function. New Delhi: Anamaya publisher.
Saxena, R.K., Pogany, T.K., Ram, J. & Daiya, J. 2011. Dirichlet Averages of Generalized Multi-index Mittag-Leffler Functions. Armenian Journal of Mathematics, 3(4), pp.174-187 [online]. Available at: http://armjmath.sci.am/index.php/ajm/article/view/79 [Accessed: 20 August 2022].
Shukla A.K. & Prajapati J.C. 2007. On a generalization of Mittag-Leffler function and its properties. Journal of Mathematical Analysis and Applications, 336(2), pp.797-811. Available at: https://doi.org/10.1016/j.jmaa.2007.03.018
Singh, D.K. & Rawat, R.A.H.U.L. 2013. Integrals involving generalized Mittag-Leffler function. Journal of Fractional Calculus and Applications, 4(2), pp.234-244 [online]. Available at: http://math-frac.org/Journals/JFCA/Vol4(2)_July_2013/Vol4(2)_Papers/07_Vol.%204(2)%20July%202013,%20No.%207,%20pp.%20234-244..pdf [Accessed: 20 August 2022].
Srivastava, H.M. & Manocha, H.L. 1984. A Treatise on Generating Functions. New York: Hasted Press.
Srivastava, H.M. & Tomovski, Ž. 2009. Fractional calculus with an integral operator containing a generalized Mittag–Leffler function in the kernel. Applied Mathematics and Computation, 211(1), pp.198-210. Available at: https://doi.org/10.1016/j.amc.2009.01.055
Wiman, A., 1905. Über den Fundamentalsatz in der Teorie der Funktionen Eυ(x). Acta Mathematica, 29, pp.191-201. Available at: https://doi.org/10.1007/BF02403202
Wright, E.M. 1935a. The Asymptotic Expansion of the Generalized Bessel Function. Proceedings of the London Mathematical Society, s2-38(1), pp.257-270. Available at: https://doi.org/10.1112/plms/s2-38.1.257
Wright, E.M. 1935b. The Asymptotic Expansion of the Generalized Hypergeometric Function. Journal of the London Mathematical Society, s1-10(4), pp.286-293. Available at: https://doi.org/10.1112/jlms/s1-10.40.286
Sva prava zadržana (c) 2022 Sirazul Haq, Maggie Aphane, Mohammad Saeed Khan, Nikola Fabiano
Ovaj rad je pod Creative Commons Autorstvo 4.0 međunarodnom licencom.
Vojnotehnički glasnik omogućava otvoreni pristup i, u skladu sa preporukom CEON-a, primenjuje Creative Commons odredbe o autorskim pravima:
Autori koji objavljuju u Vojnotehničkom glasniku pristaju na sledeće uslove:
- Autori zadržavaju autorska prava i pružaju časopisu pravo prvog objavljivanja rada i licenciraju ga Creative Commons licencom koja omogućava drugima da dele rad uz uslov navođenja autorstva i izvornog objavljivanja u ovom časopisu.
- Autori mogu izraditi zasebne, ugovorne aranžmane za neekskluzivnu distribuciju rada objavljenog u časopisu (npr. postavljanje u institucionalni repozitorijum ili objavljivanje u knjizi), uz navođenje da je rad izvorno objavljen u ovom časopisu.
- Autorima je dozvoljeno i podstiču se da postave objavljeni rad onlajn (npr. u institucionalnom repozitorijumu ili na svojim internet stranicama) pre i tokom postupka prijave priloga, s obzirom da takav postupak može voditi produktivnoj razmeni ideja i ranijoj i većoj citiranosti objavljenog rada (up. Efekat otvorenog pristupa).