Uncertain Fractional Differential Equations Research Articles

Existence and uniqueness of the solution to uncertain fractional differential equation

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.

Uncertain fractional differential equations and an interest rate model

The concept of uncertain fractional differential equation is introduced, and solutions of several uncertain fractional differential equations are presented. This kind of equation is a counterpart of stochastic fractional differential equation. By the proposed concept, an interest rate model is considered, and the price of a zero‐coupon bond is obtained. Copyright © 2014 John Wiley & Sons, Ltd.

Explicit solutions of fractional differential equations with uncertainty

We give the explicit solutions of uncertain fractional differential equations (UFDEs) under Riemann–Liouville H-differentiability using Mittag-Leffler functions. To this end, Riemann–Liouville H-differentiability is introduced which is a direct generalization of the concept of Riemann–Liouville differentiability in deterministic sense to the fuzzy context. Moreover, equivalent integral forms of UFDEs are determined which are applied to derive the explicit solutions. Finally, some illustrative examples are given.