Abstract
This paper investigates the existence of positive solutions for a class of nonlinear fractional q-difference equations with integral boundary conditions. By applying monotone iterative method and some inequalities associated with the Green’s function, the existence results of positive solutions and two iterative schemes approximating the solutions are established. An explicit example is given to illustrate the main result.
Highlights
We consider the following nonlinear fractional q-difference equation with integral boundary conditions: Dαq u(t) + h(t)f t, u(t) =, t ∈ (, ), ( . )Djqu( ) =, ≤ j ≤ n, u( ) = μ g(s)u(s) dqs, The monotone iterative method is an interesting and effective technique for investigating the existence of solutions/positive solutions for nonlinear boundary value problems
To the best of authors’ knowledge, there is still little utilization of the monotone iterative method to study the existence of positive solutions for boundary value problems of nonlinear fractional q-difference equations with integral boundary conditions
By applying the monotone iteration method, Zhang et al [ ] obtained the positive extremal solutions and iterative schemes for approximating the solution of fractional differential equations with nonlinear terms depending on the lower-order derivatives on a half-line
Summary
1 Introduction We consider the following nonlinear fractional q-difference equation with integral boundary conditions: Dαq u(t) + h(t)f t, u(t) = , t ∈ ( , ), To the best of authors’ knowledge, there is still little utilization of the monotone iterative method to study the existence of positive solutions for boundary value problems of nonlinear fractional q-difference equations with integral boundary conditions. The monotone iterative method is an interesting and effective technique for investigating the existence of solutions/positive solutions for nonlinear boundary value problems.
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