A Study on the Existence and Uniqueness of Uncertain Fractional Differential Equations with Monotone Condition

Document Type : Research Paper


1 Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran.

2 University of applied science and technology, central of peechkar, Pakdasht, Iran.

3 Department of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.

4 University of applied science and technology, central of peechkar, Varamin, Iran.


The aim of this paper is to investigate the existence and uniqueness of solutions to uncertain fractional differential equations proposed by Canonical Liu’s process. To this end, we provide and prove a novel existence and uniqueness theorem for uncertain fractional differential equations under Local Lipschitz and monotone conditions is provided and proved. This result helps us to consider and analyze solutions to a wide range of nonlinear uncertain fractional differential equations driven by Canonical’s process to be considered and analyzed.


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