Yue Liang

Bio: Yue Liang is an academic researcher from Gansu Agricultural University. The author has contributed to research in topics: Fixed-point theorem & Semigroup. The author has an hindex of 3, co-authored 5 publications receiving 16 citations.

Existence and controllability of fractional evolution equation with sectorial operator and impulse

Abstract: This paper deals with the existence and uniqueness of PC-mild solutions for fractional impulsive evolution equation involving nonlocal conditions and sectorial operators. We also study the nonlocal controllability of the control system governed by fractional impulsive evolution equation.

Monotone iterative technique for impulsive fractional evolution equations with noncompact semigroup

Abstract: This paper deals with the existence of mild solutions for a class of Caputo fractional impulsive evolution equation with nonlocal condition and noncompact semigroup. By using a monotone iterative technique in the presence of coupled lower and upper L-quasi-solutions and using Sadovskii’s fixed point theorem, some existence theorems are obtained. The discussion is based on operator semigroup theory.

Existence of positive solutions for the fractional q-difference boundary value problem

Abstract: In this paper, we investigate the existence of positive solutions for a class of fractional boundary value problems involving q-difference. By using the fixed point theorem of cone mappings, two existence results are obtained. Examples are given to illustrate the abstract results.

Existence of mild solutions for fractional nonlocal evolution equations with delay in partially ordered Banach spaces

Abstract: This paper deals with the existence of mild solutions for the abstract fractional nonlocal evolution equations with noncompact semigroup in partially ordered Banach spaces. Under some mixed conditions, a group of sufficient conditions for the existence of abstract fractional nonlocal evolution equations are obtained by using a Krasnoselskii type fixed point theorem. The results we obtained are a generalization and continuation of the recent results on this issue. At the end, an example is given to illustrate the applicability of abstract result.

Positive periodic solutions for high-order differential equations with multiple delays in Banach spaces

Abstract: This paper deals with the existence of positive ω-periodic solutions for nth-order ordinary differential equation with delays in Banach space E of the form $$L_{n}u(t)=f\bigl(t,u(t-\tau_{1}),\ldots,u(t- \tau_{m})\bigr),\quad t\in\mathbb{R}, $$ where $L_{n}u(t)=u^{(n)}(t)+\sum_{i=0}^{n-1}a_{i} u^{(i)}(t)$ is the nth-order linear differential operator, $a_{i}\in\mathbb {R}$ ($i=0,1,\ldots,n-1$) are constants, $f: \mathbb{R}\times E^{m}\rightarrow E$ is a continuous function which is ω-periodic with respect to t, and $\tau_{i}>0$ ($i=1,2,\ldots,m$) are constants which denote the time delays. We first prove the existence of ω-periodic solutions of the corresponding linear problem. Then the strong positivity estimation is established. Finally, two existence theorems of positive ω-periodic solutions are proved. Our discussion is based on the theory of fixed point index in cones.

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

Abstract: This research uses the extended exp- $( -\varphi(\vartheta ) ) $ -expansion and the Jacobi elliptical function methods to obtain a fashionable explicit format for solutions to the fragmented biological population and the same width models that depict popular logistics because of deaths or births. In mathematical terminology, the linear, hyperbolic, and trigonometric equation solutions that have been found describe several innovative aspects from the two models. Sketching these solutions in different types is used to give them more details. The accuracy and performance of the method adopted show their ability to be applied to various nonlinear developmental equations.

On fractional neutral integro-differential systems with state-dependent delay and non-instantaneous impulses

Abstract: In this manuscript, we work to actualize the Darbo (Banas and Goebel in Measure of Noncompactness in Banach Space. Lecture Notes in Pure and Applied Mathematics, 1980) fixed point theorem (FPT) coupled with the Hausdorff measure of non-compactness to analyze the existence results for an impulsive fractional neutral integro-differential equation (IFNIDE) with state-dependent delay (SDD) and non-instantaneous impulses (NII) in Banach spaces. Finally, examples are offered to demonstrate the concept.

Periodic boundary value problems for impulsive conformable fractional integro-differential equations

Abstract: This paper is concerned with the existence of solutions for periodic boundary value problems for impulsive fractional integro-differential equations using a recent novel concept of conformable fractional derivative. We give a new definition of exponential notations and impulsive integrals for constructing the Green function and a comparison result of the linear problems with impulses. By applying the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, some new sufficient conditions for the existence of solutions are established. The obtained results are well illustrated by an example.

Approximation theorems for controllability problem governed by fractional differential equation

Abstract: In this manuscript, we discuss the optimal control problem for a nonlinear system governed by the fractional differential equation in a separable Hilbert space \begin{document}$ X $\end{document} . We utilize the fixed point technique and \begin{document}$ \eta $\end{document} -resolvent family to present the existence of control for the fractional system. The optimal pair is obtained as the limit of the optimal pair sequence of the unconstrained problem. Further, we derive some approximation results, which guarantee the convergence of the numerical method to optimal pair sequence. Finally, the main results are validated with the aid of an example.

Positive Solution of Singular Nonlinear Third Order Periodic Boundary Value Problem

Abstract: We considered nonlinear singular third order periodic boundary value problem{u″'+ρ3u=f(t,u),t∈I=(0,2π),ρ∈(0,1/3~(1/2))u(i)(0)=u(i)(2π),i=0,1,2 and obtained positive solution under some conditions concern to the eigenvalue of relevant linear operator by fixed index theory on cone.