The existence and uniqueness of a class of fractional differential equations
Summary: By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, \(D_{0 +}^q x(t) = f(t, x(t), D_{0 +}^{q - 1} x(t)), t \in(0, T), \)\(x(0) = 0, D_{0 +}^{q - 1} x(0) = x_0, \) are discussed, where \(f \in C([0, T] \times \mathbb{R}^2, \mathbb{R}), D_{0 +}^q x(t)\) is the standard Riemann-Liouville fractional derivative, \(1 < q < 2\). Some mistakes in the literature are pointed out and some new inequalities and existence and uniqueness results are obtained.
scientific article; zbMATH DE number 7022469
scientific article