Document Type : Research Paper
Authors
- Devaraj Vivek ^{1}
- Omid Baghani ^{} ^{2}
- Kuppusamy Kanagarajan ^{1}
^{1} Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
^{2} Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
Abstract
We develop the theory of hybrid fractional differential equations with the complex order $\theta\in \mathbb{C}$, $\theta=m+i\alpha$, $0<m\leq 1$, $\alpha\in \mathbb{R}$, 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.
Keywords
- Hybrid fractional differential equations
- Initial value problem
- Complex order
- Dhage's fixed point theorems
- Existence of mild solution
Main Subjects
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