New mixed operators for fractional integrations with some applications

{Mohamed Bezziou; Zoubir Dahmani; Mehmet Zeki Sarikaya; Iqbal Jebril

{Mohamed Bezziou UDBKM, University and laboratory LPAM, Mostaganem, Algeria.
Zoubir Dahmani Laboratory LPAM, Faculty of SEI, UMAB, University of Mostaganem, Algeria
Mehmet Zeki Sarikaya Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-TURKEY
Iqbal Jebril Mathematics Department, Al Zaytoonah University of Jordan, \\ Queen Alia Airport St 594, Amman 11733, Jordane

Abstract

In this paper, we introduce new mixed operators related to the coupled orders Riemann-Liouville integrals. Then, we prove some of their properties, such as semigroup and commutativity. At the end, some applications are discussed.