پیوندهای مفید
آمار
| تعداد نشریات | 30 |
| تعداد شماره‌ها | 426 |
| تعداد مقالات | 3,753 |
| تعداد مشاهده مقاله | 5,903,517 |
| تعداد دریافت فایل اصل مقاله | 4,095,373 |
Mellin-Sumudu Synergy: A Novel Paradigm for Extending Mittag-Leffler Function | ||
| Journal of Hyperstructures | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 شهریور 1404 اصل مقاله (1.66 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.16472.1069 | ||
| نویسندگان | ||
| Mousmi Kulmitra1؛ Omprakash Dewangan* 2 | ||
| 11Department of Mathematics, Govt. Rajmata Vijaya Raje Sindhiya Kanya Mahavidyalaya Kawardha, Dist.- Kabirdham (C.G.), India | ||
| 2Indira Gandhi Govt. College Pandaria, Distt.- Kabirdham, Hemchand Yadav Vishwavidyalaya Durg, Chhattisgarh, India | ||
| چکیده | ||
| This study presents an innovative reconfiguration of the Mittag-Leffler function (MLF) by synergistically combining the Mellin transform and the Sumudu transform. Although the MLF plays a significant role in fractional calculus, its complexity has limited its applicability. By utilizing both the Mellin and Sumudu transforms, new integral representations of the MLF are derived, effectively broadening its scope in addressing fractional differential equations. This integrated approach provides a deeper understanding of the MLF’s properties and enables its extension to a wider range of problems in physics, engineering, and mathematics. The effectiveness of the proposed extension is demonstrated through its application to fractional calculus problems, thereby contributing to the advancement of the field and enhancing its ability to model complex real-world phenomena with greater accuracy. | ||
| کلیدواژه‌ها | ||
| Mittag-Leffler Function (MLF)؛ Mellin Transform (MF)؛ Sumudu Transform (ST)؛ Fractional Calculus؛ Integral Transforms | ||
| مراجع | ||
|
[1] M. Arshad, J. Choi, S.Mubeen, K. S. Nisar and G. Rahman, A new extension of Mittag-Leffler function, Commun. Korean Math. Soc 33(2) (2018), 549–560. [2] U. Ayub, S. Mubeen,T. Abdel jawad,G. Rahman and K.S. Nisar, The new Mittag-Leffler function and it’s applications, J. of Math., 5(1), (2020),1–8. [3] R.A. Cerutti, L.L. Luque and G.A. Dorrego, on the (p − k) Mittag - Leffler function, Appl. Math. Sci., 11 (2017), 2541–2566. [4] V.S. Dhakar and K. Sharma, On a recurrence relation of K-Mittag-Leffler function, Commun. Korean Math. Soc., 28(4) (2013), 851–856. [5] R. Diaz and E. Pariguan, on hypergeometric function and k- pochhammersymbol, Div. Math. 15(2) (2007), 179–192. [6] G.A. Dorrego and R.A. Cerutti, The k-Mittag Leffler function, Int. J. Contemp. Math. Sci., 7(15) (2012), 705–716. [7] N.J. Fine, Note on the Hurwitz zeta-function Proc. Amer. Math. Soc.,Vol. 2 (1951), 361–364. [8] K.S. Gehlot, Multiparameter K-Mittag-Leffler Function, Int. Math. Forum, 8(34) (2013), 1691 – 1702. [9] K.S. Gehlot, The p-k Mittag-Leffler function. Palest. J. Math., 7(2) (2018), 628–632. [10] K.S. Gehlot and A. Bhandari, The J-Generalized P-K Mittag-Leffler Function, J. Fract. Calc. Appl., 13(1) (2022), 122–129. [11] K.S. Gehlot and K. Nantomah, p−q−k gamma and beta functions and their properties, IJPAM, 118(3) (2018), 525–533. [12] I. Grattan-Guinness, M.G. Mittag-Leffler, Materials for the history of mathematics in the Institut Mittag-Leffler, Isis 62(3) (1971), 363–374. [13] ¨ O. G¨urel Yılmaz, R. Akta¸s and F. Ta¸sdelen On some formulas for the k-analogue of Appell functions and generating relations via k-fractional derivative, Fract. Fract., 4(4) (2020), p. 48. [14] R. D´ıaz, C. Ortiz and E. Pariguan, On the k-gamma q-distribution, Open Math., 8(3) (2010), 448–458. [15] F. Mainardi, On some properties of the Mittag-Leffler function Eα(−tα), completely monotone for t > 0 with 0 < α < 1 arXiv preprint arXiv, 1305.0161, (2013). [16] Mittag-Leffler, G¨osta Magnus. la nouvelle fonction Eα(x). CR Acad. Sci. Paris 137(2) (1903), 554–558. [17] K.S. Nisar, S.D. Purohit, M.S. Abouzaid, M.A. Qurashia and D. Baleanu, Generalized k-Mittag-Leffler function and its composition with pathway integral operators, J. Nonlinear Sci. Appl 9(6) (2016), 3519–3526. [18] T.R. Prabhakar, A singular integral equation with a generalized Mittag- Leffler function in the kernel, Yokohama Math. J. 19 (1971), 7–15. [19] R. Rahman, I. Suwan, K. Nisar, T. Abdeljawad, S. Samraiz and A. Ali, A basic study of a fractional integral operator with extended Mittag-Leffler kernel, AIMS, 2021. [20] H.M. Srivastava, ˇZ. Tomovski Fractional calculus with an integral operator containing a generalized Mittag–Leffler function in the kernel, Appl. Math. Comput., 211(1) (2009), 198–210. [21] E.C. Titchmarsh, The theory of the Riemann zeta-function. The Clarendon Press Oxford University Press, 1986. [22] G.K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. Educ., 24(1) (1993), 35–43. [23] A. Wiman, Uber den fundamental Satz in der theorie der funktionen Eα(z), Acta Math. 29 (1905),191–201. | ||
|
آمار تعداد مشاهده مقاله: 33 تعداد دریافت فایل اصل مقاله: 158 |
||