The Marichev-Saigo-Maeda fractional calculus operator pertaining to the generalized multivariate Mittag-Leffler function
*Pranjali GautamCorresponding authorpranjalig62@gmail.comDepartment of MathematicsGharuanChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Harish Nagardrharishngr@gmail.comDepartment of MathematicsGharuanChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Sonia Sharmaskaushiksonia96@gmail.comDepartment of MathematicsGharuanChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile →
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- Received:
- 09 Jul 2024
- Published Online:
- 16 Dec 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2050
- Pages:
- 1853–1860
Abstract
Keywords
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References
[1] G. M. Mittag-Leffler, “Sur la nouvelle fonction E_α(x),” C. R. Acad. Sci. Paris, vol. 137, no. 2, pp. 554–558 (1903).
[2] T. R. Prabhakar, “A singular integral equation with a generalized Mittag-Leffler function in the kernel,” Yokohama Mathematical Journal, vol. 19, no. 1, pp. 7–15 (1971).
[3] R. K. Saxena, S. L. Kalla, and R. Saxena, “Multivariate analogue of generalized Mittag-Leffler function,” Integral Transforms and Special Functions, vol. 22, no. 7, pp. 533–548 (2011).
[4] A. Wiman, “Über den Fundamentalsatz in der Theorie der Funktionen E_α(x),” (1905).
[5] O. I. Marichev, “Volterra equation of Mellin convolution type with a Horn function in the kernel,” Izvestiya Akademii Nauk BSSR, Seriya Fiziko-Matematicheskikh Nauk, vol. 1, pp. 128–129 (1974).
[6] M. Saigo and N. Maeda, “More generalization of fractional calculus,” in Transform Methods and Special Functions, Varna, Bulgaria, pp. 386–400 (1996).
[7] A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, vol. 3 (1990).
[8] G. Rahman, M. Samraiz, M. A. Alqudah, and T. Abdeljawad, “Multivariate Mittag-Leffler function and related fractional integral operators,” AIMS Mathematics, vol. 8, no. 6, pp. 13276–13293 (2023).
[9] H. Nagar and S. Sharma, “Applications of complex SEE integral transform,” Journal of Science and Arts, vol. 24, no. 1, pp. 163–172 (2024).
