The generalized conformable derivative for 4α-order Sturm-Liouville problems

نویسندگان
Dastmalchi Saei, Farhad ID 1
Jahangiri Rad, Mohammad ID 2
Jafari, Mohammad ID 3
Jodayree Akbarfam, Ali Asghar ID 4

1 Department of Science, Payame Noor University, PO BOX 19395-3697 Tehran, Iran.

2 Department of Applied Mathematics, Mathematical Science Faculty, University of Tabriz, Tabriz, Iran.

3 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

4 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

doi
10.22034/cmde.2021.45363.1908
چکیده

In this paper, we discuss the new generalized fractional operator. This operator similarly conformable derivative satisfies properties such as the sum, product/quotient, and chain rule. Laplace transform is defined in this case, and some of its properties are stated. In the following, the Sturm-Liouville problems are investigated, and also eigenvalues and eigenfunctions are obtained. 

کلیدواژه‌ها
Fractional Sturm-Liouville, Conformable derivative, Mittag-Leffler functions, eigenvalues