Baleanu, DumitruMohammadi, HakimehRezapour, Shahram2020-04-292020-04-292013Baleanu, Dumitru...et al. (2013). "The Existence of Solutions For a Nonlinear Mixed Problem of Singular Fractional Differential Equations", Advances In Difference Equations.1687-1847http://hdl.handle.net/20.500.12416/3526By using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem (c)D(alpha)u(t) = f(t, u(t), u'(t), (c)D(beta)u(t)), u(0) = au(1), u'(0) = b(c)D(beta)u(1), u ''(0) = u'''(0) = u((n-1))(0) = 0, where n >= 3 is an integer, alpha is an element of (n - 1, n), 0 < beta < 1, 0 < a < 1, 0 < b < Gamma (2 - beta), f is an L-q-Caratheodory function, q > 1/alpha-1 and f(t,x,y,z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, D-c stands for the Caputo fractional derivative.eninfo:eu-repo/semantics/openAccessBoundary Value ProblemFixed PointFractional Differential EquationGreen FunctionRegularizationSingularArticle10.1186/1687-1847-2013-359