Existence and Uniqueness for a Nonlinear Fractional Differential Equation

Some existence results on nonlinear fractional differential equations

“…The field of fractional differential equations has been subjected to an intensive development of theory and applications ( [1][2][3][4][5][6][7][8][9] and references therein). For a new history of fractional calculus, see Machado et al [10].…”

Some New Uniqueness Results of Solutions to Nonlinear Fractional Integro-Differential Equations

“…In latest years, there has been an interest in the look at of the theory fractional differential equations, it has seen significant improvement, see as an instance the monographs of Delboso and Rodino [8], Diethelm [9], Kilbas et al [10], Miller and Ross [11] Oldham and Spanier [13] and the references therein. Recently, uniqueness standards for the various fractional integro-differential equations have been taken into consideration by way some authors, for greater info, (see [1,2,3,4,5,6,7,12,16] …”

Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation

“…Recently, there are some papers dealing with the existence and multiplicity of solutions of nonlinear initial value fractional differential equation by the use of techniques of nonlinear analysis [2,3,5,6]. In [3] and [6], the authors considered the Dirichlet-type boundary value problem for fractional differential equations D α 0 + u(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = u(1) = 0, (1.1) where 1 < α 2 is a real number and D α 0 + is the standard Riemann-Liouville derivative, and f : [0, 1] × [0, ∞) → [0, ∞) is continuous.…”