Solving existence results in multi-term fractional differential equations via fixed points

Many researchers are interested in the existence theory of solutions to fractional differential equations. In the literature, existence results have been obtained by using a variety of fixed point problems, including the fixed-point problems of Lefschetz, Kleene, Tychonoff, and Banach. In this article, we propose a generalized version of the contraction principle in the context of controlled rectangular metric space. With this result, we address the existence and uniqueness results for the following fractional-order differential equations. 1. The nonlinear multi-term fractional delay differential equation [GRAPHICS] where, [GRAPHICS] and D-c(delta) denotes the Caputo fractional derivative of order delta. 2. The Caputo type fractional differential equation [GRAPHICS] with [GRAPHICS]

Automated summary

This article discusses the existence theory of solutions to fractional differential equations. Existence results have been obtained using various fixed point problems including Lefschetz, Kleene, Tychonoff, and Banach. The article also proposes a generalized version of the contraction principle in the context of controlled rectangular metric space and applies it to discuss the existence and uniqueness results of two fractional-order differential equations.