Abstract
The paper proves an existence and uniqueness theorem of the solution to an uncertain fractional differential equation by Banach fixed point theorem under Lipschitz and linear growth conditions. Then, the paper presents an existence theorem for the solution of an uncertain fractional differential equation by Schauder fixed point theorem under continuity condition.
Highlights
Fractional differential equation has been a classical research field of differential equations
We only prove the theorem for the uncertain fractional differential equation (2)
Since Xt,k are uncertain vectors for k = 1, 2, · · ·, we know that Xt is an uncertain vector by Theorem 3 in the Appendix. It follows from the arbitrariness of T > 0 that Xt is the unique solution of uncertain fractional differential equation (2)
Summary
Fractional differential equation has been a classical research field of differential equations. The solutions were provided by the Mittag-Leffler function for linear uncertain fractional differential equations. We will show the existence and uniqueness of solutions for uncertain fractional differential equations.
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