Positive Solutions of the Fractional Relaxation Equation Using Lower and Upper Solutions

Linear and Nonlinear Fractional Voigt Models

“…In this section, motivated by many papers that discuss the existence of solutions to initial value problems, e.g. [5,6,12], we focus on the fractional initial value problem (10). ǫ .…”

Existence and uniqueness of positive solutions for first-order nonlinear Liouville–Caputo fractional differential equations

“…Fractional differential equations with and without delay arise from a variety of applications including in various fields of science and engineering such as applied sciences, practical problems concerning mechanics, the engineering technique fields, economy, control systems, physics, chemistry, biology, medicine, atomic energy, information theory, harmonic oscillator, nonlinear oscillations, conservative systems, stability and instability of geodesic on Riemannian manifolds, dynamics in Hamiltonian systems, etc. In particular, problems concerning qualitative analysis of linear and nonlinear fractional differential equations with and without delay have received the attention of many authors, see [1][2][3][4][5][6][7][8][9][10][11][12]14] and the references therein.…”

Positive solution of a fractional differential equation with integral boundary conditions

“…Many interesting results of the existence of positive solutions of various classes of fractional differential equations with or without the integral boundary condition have been discussed. Among these works (see [6][7][8][9][10][11][12][13][14][15][16][17]) and the references therein. For example in [12], Nan and Wang studied the existence and uniqueness of a positive solution for the following nonlinear fractional differential equations where 0 < α < 1, D α 0 + is the standard Riemann-Liouville fractional derivative and f : [0, 1] × R + −→ R + is continuous.…”