Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

Abstract

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

Existence Result for a Superlinear Fractional Navier Boundary Value Problems

“…First, we recall in the following lemma due to [19] some estimates on the Green function H(x, t) and properties of the associated potential kernel defined by 1)) and x ∈ (0, 1). …”

“…The theory of fractional differential equations with various boundary conditions has been developed very quickly and the investigation for the existence, uniqueness and asymptotic behavior of positive continuous solutions attracted a considerable attention of researches ( see [1][2][3][4]6,7,13,15,[17][18][19]21,22,25,29,30] and the references therein ).…”

“…Later, in [19], Mâagli and Dhifli studied the following sublinear fractional Navier boundary value problem:…”

Existence and exact asymptotic behaviour of positive solutions for fractional boundary value problem with P-Laplacian operator

“…for some η > 1, where c > 0 and z is a continuous function on [0, η], with z(0) = 0. To describe the result of [13] in more details, we need some notations.…”

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

“…It is worth mentioning that many authors studied fractional differential equations which were applied in many fields such as physics, mechanics, chemistry, and engineering; (see, for instance [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and the references therein).…”