New uniqueness results for fractional differential equations

Abstract

We develop the Krasnoselskii–Krein type of uniqueness theorem for an initial value problem of the Riemann–Liouville type fractional differential equation which involves a function of the form f (t, x(t), D ^q−1 x(t)), for 1<q<2 and establish the convergence of successive approximations. We prove a few other uniqueness theorems.

Keywords:

• fractional differential equations
• uniqueness theorems
• successive approximations

AMS Subject Classifications::

• 34A08
• 34A12
• 26A33

Acknowledgements

Fulya Yoruk acknowledges the financial support by the Council of Higher Education, Turkey, for making the visit to Florida Tech possible. She also, thanks the Department of Mathematical Sciences, for all the help she was given during her stay at Florida Tech.