Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative

Abstract

In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.