Generalized Riemann-Liouville and Liouville-Caputo time fractional evolution equations associated to the number operator

São Paulo Journal of Mathematical Sciences - Tập 15 - Trang 435-449 - 2021
Ziyad A. Alhussain1, Habib Rebei2, Hafedh Rguigui3,4, Anis Riahi1
1Department of Mathematics, College of Science of Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia
2Department of Mathematics, College of Science, Qassim University Buraidah, Saudi Arabia.
3Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al-Qunfudhah, Saudi Arabia
4Department of Mathematics, Higher School of Sciences and Technologies of Hammam-Sousse, Sousse, University, Sousse, Tunisia

Tóm tắt

By means of the Laplace transform, we give the solution of the generalized Riemann-Liouville and Liouville-Caputo time fractional evolution equations in infinite dimensions associated to the number operator. These solutions are given in terms of the Mittag-Leffler function and the convolution product.

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