Existence and stability analysis of solutions for a new kind of boundary value problems of nonlinear fractional differential equations

This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed

Positive solutions of superlinear semipositone singular Dirichlet boundary value problems

AbstractIn this paper, we study a class of superlinear semipositone singular second order Dirichlet boundary value problem. A sufficient condition for the existence of positive solution is obtained under the more simple assumptions

Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay

This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field

Positive solutions of higher order fractional integral boundary value problem with a parameter

In this paper, we study a higher-order fractional differential equation with integral boundary conditions and a parameter. Under different conditions of nonlinearity, existence and nonexistence results for positive solutions are derived in terms of different intervals of parameter. Our approach relies on the Guo–Krasnoselskii fixed point theorem on cones

Uniqueness of iterative positive solutions for the singular infinite-point p-Laplacian fractional differential system via sequential technique

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results

Cellular Automata Model for Traffic Flow with Optimised Stochastic Noise Parameter

Based on the existing safe distance cellular automata model, an improved cellular automata model based on realistic human reactions is proposed in this paper, which aims to reproduce the characteristics of congested traffic flow. In the proposed model, the stochastic noise param-eter is optimised by considering driving behavioural dif-ference. The relative speed, gap and acceleration of the front vehicle are introduced into the optimised stochastic noise parameter oriented to describing the asymmetric acceleration behaviour of drivers in congestion. The sim-ulation results show that an uneven distribution of accel-eration trajectories of vehicles experiencing congestion exhibited on the spatial-temporal diagram of the pro-posed model is reproduced. Based on the analysis of the NGSIM, compared with the model with traditional sto-chastic noise parameter, the vehicles that move accord-ing to the proposed model can follow more easily and more realistically. Then the actual gap of vehicles can be better reflected by the proposed model and the change of vehicle speed is more stable. Additionally, the traffic efficiency from two aspects of flow and speed shows that the proposed model can significantly improve the traffic efficiency in the medium high density region

Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable

Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters

In this paper, we study the existence of a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters. By using the properties of the Green’s function and the Guo-Krasnosel’skii fixed point theorem, we obtain some existence results of positive solutions under some conditions concerning the nonlinear functions. The method of this paper is a unified method for establishing the existence of positive solutions for a large number of nonlinear differential equations with coupled boundary conditions. In the end, examples are given to demonstrate the validity of our main results

The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces

We prove that Fan's theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors