@article { author = {Noroozi, Hossein and Ansari, Alireza}, title = {Basic results on distributed order fractional hybrid differential equations with linear perturbations}, journal = {Journal of Mathematical Modeling}, volume = {2}, number = {1}, pages = {55-73}, year = {2014}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {}, abstract = {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}, keywords = {Fractional hybrid differential equations,distributed order,extremal solutions,Banach algebra}, url = {https://jmm.guilan.ac.ir/article_102.html}, eprint = {https://jmm.guilan.ac.ir/article_102_b82e26b4e06c58afab2f6423d030cb3c.pdf} }