Existence, uniqueness, and multiplicity results on positive solutions for a class of Hadamard‐type fractional boundary value problem on an infinite interval

Abstract

This paper focuses on a class of Hadamard‐type fractional differential equation with nonlocal boundary conditions on an infinite interval. New existence, uniqueness, and multiplicity results of positive solutions are obtained by using Schauder's fixed point theorem, Banach's contraction mapping principle, the monotone iterative method, and the Avery‐Peterson fixed point theorem. Examples are included to illustrate our main results.

New results for higher‐order Hadamard‐type fractional differential equations on the half‐line

“…But as far as we know, many results are obtained for the Hadamard-type fractional boundary value problem using either m-point fractional integral boundary condition or integral boundary condition, see previous works. [18][19][20][21][22][23][24][25][26][27][28][29][30] Thiramanus et al 19 investigated the following boundary value problem:…”

Existence and Ulam's type stability results for a class of fractional boundary value problems on a star graph

“…The extensive application of fractional calculus has made people pay increasing attention to solving fractional differential equations with boundary or initial conditions, and the main methods used are fixed point theory, coincidence degree theory, the variational method, the monotone iterative method, and the upper and lower solution method (see other studies [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and the references therein).…”

Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

“…In recent years, the discussion of fractional initial value problems (IVPs) and BVPs have attracted the attention of many scholars and valuable results have been obtained (see ). Various methods have been utilized to study fractional IVPs and BVPs such as the Banach contraction map principle (see [8][9][10][11]), fixed point theorems (see [12][13][14][15][16][17][18]), monotone iterative method (see [19][20][21]), variational method (see [22][23][24]), fixed point index theory (see [17][18][19][20][21][22][23][24][25]), coincidence degree theory (see [26][27][28][29]), and numerical methods [30,31]. For instance, Jiang (see [26]) studied the existence of solutions using coincidence degree theory for the following fractional BVP:…”

“…Numerous papers discuss BVPs of integer-order differential equations on infinite intervals (see [35][36][37][38]). Naturally, BVPs of fractional differential equations on infinite intervals have received some attention (see [8,12,[14][15][16][18][19][20]27,29,32]). For example, Wang et al [8] considered the following fractional BVPs on an infinite interval:…”