Uniqueness of positive solutions for a perturbed fractional differential equation
Summary: We are concerned with the existence and uniqueness of positive solutions for the nonlinear perturbed fractional two-point boundary value problem \[ D^\alpha_{0+} u(t) + f(t, u, u', \dotsc, u^{(n-2)}) + g(t) = 0,\quad 0 < t < 1,\;n - 1 < \alpha \leq n,\;n \geq 2, \] \[ u(0) = u'(0) = \dotsb = u^{(n-2)}(1) = 0, \] where \(D^\alpha_{0+}\) is the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem of generalized concave operators. An example is given to illustrate the main result.
scientific article; zbMATH DE number 6134547
scientific article