Multiple positive solutions of a singular fractional differential equation with negatively perturbed term

New Result on the Critical Exponent for Solution of an Ordinary Fractional Differential Problem

“…On the other hand, fractional order integral and derivative operators are nonlocal which can describe the behaviour of many complex processes and systems with long-memory in time. This implies that fractional order models possess much more advantage than integer order models, especially in viscoelasticity, electrochemistry, and porous media [11][12][13][14][15], and many new applications for fractional models in various fields have also been reported recently [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

The Existence of Solutions to Integral Boundary Value Problems of Fractional Differential Equations at Resonance

“…In [4], the authors studied the existence of positive solutions for the nonresonant case by Krasnosel'skii's fixed point theorem. In [5], the author investigated the uniqueness of solutions for the nonresonant case by use of the 0 -positive operator under a Lipschitz condition on .…”

“…In present, many papers are devoted to the integral boundary value problem for fractional differential equation under nonresonance conditions; see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. On the other hand, there are some papers studying integral boundary value problem for differential equation under resonant conditions; we refer the reader to [21][22][23][24][25][26][27][28][29].…”

Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation

“…Generally, some perturbations and uncertainties usually exist in these real world differential models due to some uncertain physical parameters and parametrical variations in time. These perturbations and uncertainties can be introduced in the underlying mathematical model [3,5,7,9,10,15,16,18].…”