Existence and uniqueness of solutions for a nonlinear fractional initial value problem involving Caputo derivatives. (English) Zbl 1462.47050
Summary: In this paper, we give a sufficient condition for the existence and uniqueness interval of continuous solutions to a class of fractional initial value problems involving Caputo derivatives when the data functions satisfy a non-classical Lipschitz condition. The main tool used in the paper is a fixed point theorem for generalized contractions due to Browder-Matkowski [F. E. Browder, Nederl. Akad. Wet., Proc., Ser. A 71, 27–35 (1968; Zbl 0155.19401); J. Matkowski, Diss. Math. 127 (1975; Zbl 0318.39005)].
MSC:
| 47N20 | Applications of operator theory to differential and integral equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
