In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $\varphi$-Lipschitz and Caratheodory conditions. Some basic fractional differential inequalities of distributed order are utilized to prove the existence of extremal solutions and comparison principle
Noroozi, H., & Ansari, A. (2014). Basic results on distributed order fractional hybrid differential equations with linear perturbations. Journal of Mathematical Modeling, 2(1), 55-73.
MLA
Hossein Noroozi; Alireza Ansari. "Basic results on distributed order fractional hybrid differential equations with linear perturbations". Journal of Mathematical Modeling, 2, 1, 2014, 55-73.
HARVARD
Noroozi, H., Ansari, A. (2014). 'Basic results on distributed order fractional hybrid differential equations with linear perturbations', Journal of Mathematical Modeling, 2(1), pp. 55-73.
VANCOUVER
Noroozi, H., Ansari, A. Basic results on distributed order fractional hybrid differential equations with linear perturbations. Journal of Mathematical Modeling, 2014; 2(1): 55-73.
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