# Search results

Advances in Difference Equations > 2019 > 2019 > 1 > 1-12

Mediterranean Journal of Mathematics > 2019 > 16 > 5 > 1-16

*q*-derivative: $$\begin{aligned}&D_q^\alpha u(t)+f(t,u(t),u(t))+g(t,u(t))=0, \quad 0<t<1 ,\\&u(0)=0 ,\quad u(1)=\beta u(\eta ), \end{aligned}$$ Dqαu(t)+f(t,u(t),u(t))+g(t,u(t))=0,0<t<1,u(0)=0,u(1)=βu(η), where $$D_q^\alpha $$ Dqα is the fractional...

Advances in Difference Equations > 2018 > 2018 > 1 > 1-15

*q*-derivative: Dqαu(t)+f(t,u(t),u(t))+g(t,u(t))=0,0<t<1,u(0)=Dqu(0)=0,u(1)=μ∫01u(s)dqs, $$\begin{aligned} &D_{q}^{\alpha}u(t)+f\bigl(t,u(t),u(t)\bigr)+g\bigl(t,u(t) \bigr)=0, \quad 0< t< 1, \\ & u(0)=D_{q}u(0)=0, \qquad u(1)=\mu \int_{0}^{1}u(s)\,d_{q}s,...

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 4 > 1507-1521

*q*-difference equation boundary value problem. The main results show that we can construct an iterative scheme approximating the unique...

Advances in Difference Equations > 2017 > 2017 > 1 > 1-13

*q*-difference equation. By using the monotone iterative technique and lower-upper solution method, we get the existence of positive or negative solutions under the nonlinear term is local continuity and local monotonicity. The results show that we can construct two iterative sequences for approximating the solutions.

Journal of Applied Mathematics and Computing > 2017 > 55 > 1-2 > 353-367

*q*-derivative $$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$ D q α u ( t ) + f ( t , u...

Boundary Value Problems > 2016 > 2016 > 1 > 1-19

*q*-integral boundary value problems of a nonlinear fractional

*q*-difference equation and a nonlinear fractional

*q*-integrodifference equation. Our problems contain different numbers of order and

*q*in derivatives and integrals. The existence and uniqueness results are based on Banach’s contraction mapping principle and Krasnoselskii’s...

Advances in Difference Equations > 2015 > 2015 > 1 > 1-12

*q*-difference boundary value problem by using the

*p*-Laplacian operator: D q γ ( ϕ p ( D q δ y ( t ) ) ) + f ( t , y ( t ) ) = 0 $D_{q}^{\gamma}(\phi_{p}(D_{q}^{\delta}y(t)))+f(t,y(t))=0$ ( 0 < t < 1 ; 0 < γ < 1 ; 3 < δ <...

Journal of Applied Mathematics and Computing > 2013 > 42 > 1-2 > 89-102

*q*-fractional boundary value problem. We not only obtain the existence and uniqueness of positive solutions, but also establish the iterative schemes for approximating the solutions, which is benefit for computation and application.

Advances in Difference Equations > 2013 > 2013 > 1 > 1-15

*q*-integral boundary value problems of fractional

*q*-difference equations. By applying the generalized Banach contraction principle, the monotone iterative method, and Krasnoselskii’s fixed point theorem, some existence results of positive solutions are obtained. In addition, some examples to illustrate our results are given...

Boundary Value Problems > 2013 > 2013 > 1 > 1-16

*q*-difference equations with nonhomogeneous boundary conditions. By applying the classical tools from functional analysis, sufficient conditions for the existence of single and multiple positive solutions to the boundary value problem are obtained in term of the explicit intervals for the nonhomogeneous term. In addition, some examples to illustrate our...