Svatoslav Staněk

Existence Results for Implicit Fractional Differential Equations with Nonlocal Boundary Conditions

abstract:
We discuss the existence of solutions to the implicit fractional differential equation ${}^c\kern -2pt D^{\alpha}u = f(t,u, u',{}^c\kern -2pt D^{\beta}u,{}^c\kern -2pt D^{\alpha}u)$ satisfying nonlocal boundary conditions.
Here $1<\beta <\alpha \le 2$, $f$ is continuous and ${}^c \kern -2pt D$ is the Caputo fractional derivative. The existence results are proved by the Leray-Schauder degree method.

Mathematics Subject Classification: 34A08, 26A33, 34B15

Key words and phrases: Implicit fractional differential equation, nonlocal condition, Leray-Schauder degree, Caputo fractional derivative