Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

Abstract

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder's fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition

“…Fractional calculus is an excellent tool for the description of the process of mathematical analysis in various areas of finance, physical systems, control systems and mechanics, and so forth [1][2][3][4][5]. Many methods are used to study various fractional differential equations, such as fixed point index theory [6], iterative method [7][8][9], theory of linear operator [10,11] sequential techniques, and regularization [12], fixed point theorems [13][14][15][16][17], the Mawhin continuation theorem for resonance [18][19][20][21][22], the variational method [23]. The definition of the fractional order derivative used in the aforementioned results is either the Caputo or the Riemann-Liouville fractional order derivative.…”

A Schrödinger-type algorithm for solving the Schrödinger equations via Phragmén–Lindelöf inequalities

“…y k = u(x k+1 )u(x k ) and s k = x k+1x k . This Schrödinger Phragmén-Lindelöf method can possess the global convergence without the nondegeneracy (see [1,7,11,26] etc. ), which shows that this paper made a further progress in theory.…”

On the Generalization of a Solution for a Class of Integro-Differential Equations with Nonseparated Integral Boundary Conditions

“…Integral boundary conditions have various applications in applied fields such as blood flow problems, chemical engineering, thermoelasticity, underground water flow, and population dynamics. For a detailed description of some recent work on the integral boundary conditions, we refer the reader to some recent papers [33][34][35] and the references therein [36][37][38][39].…”