Modeling and analysis of an implicit fractional order differential equation with multiple first-order fractional derivatives and non-local boundary conditions

In recent years, researchers have investigated boundary value problems of single terms and, in rare circumstances, multi-term fractional differential equations. Nonetheless, differential equations containing more than one fractional differential operator of the implicate type must be formulated in some cases. Therefore, bearing in mind the significance of multi-term fractional order in the study of implicit differential equations, we propose a novel implicit kind of multi-terms fractional delay differential equations (MFDDEs) supplemented with non-local boundary conditions. In addition, using common fixed point theorems, conditions for the existence and uniqueness of the solution will be created. Moreover, investigations correlated to Ulam's type of stability will also be the focus of our consideration. The significance of the newly formulated delay type of fractional order differential equation with implicit behavior and non-local boundary conditions will then be demonstrated using an example.