Theory of Hybrid Fractional Differential Equations with Complex Order
نویسندگان
چکیده مقاله:
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.
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عنوان ژورنال
دوره 15 شماره 1
صفحات 65- 76
تاریخ انتشار 2019-07-01
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