Theory of Hybrid Fractional Differential Equations with Complex Order

• Main Authors: Devaraj Vivek, Omid Baghani, Kuppusamy Kanagarajan
• Format: Article
• Language: English
• Published: University of Maragheh 2019-07-01
• Series: Sahand Communications in Mathematical Analysis
• Subjects: Hybrid fractional differential equations; Initial value problem; Complex order; Dhage's fixed point theorems; Existence of mild solution
• Online Access: http://scma.maragheh.ac.ir/article_34967_a19fd276ba6778bbb6bed7f43599acca.pdf
• ISSN: 2322-5807; 2423-3900

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schr"odinger equation with complex order is given.