Nonnegative solution for singular nonlinear fractional differential equation with coefficient that changes sign

AbstractIn this paper, we consider the existence of nonnegative solutions of initial value problem for singular nonlinear fractional differential equation $$D^{s} u(t)=\lambda a(t)f(u, D^{\alpha} u), u(0) = 0, 0 < t \leq 1, 0 < \alpha < s < 1$$ where Ds and Dα are the standard Riemann-Liouville fractional derivatives, $$f : [0,\infty) \times (-\infty,+\infty) \rightarrow [0,+\infty), a : (0,1] \rightarrow R$$, may be change sign, tra : [0,1] → R, 0 ≤ r < s − α, and λ > 0 is a parameter. Our analysis relies on the Schauder fixed point theorem.