Document Type : Research Paper
Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
Department of Science, Payame Noor University, PO BOX 19395-3697 Tehran, Iran.
Department of Applied Mathematics, Mathematical Science Faculty, University of Tabriz, Tabriz, Iran.
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.