This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, the existence and uniqueness of solutions to LFPDEs were proved and then two schemes known as the basic method (BM) and modified local fractional variational iteration method (LFVIM) were developed to solve the local fractional PDEs. Multiple studies have been reported in the literature to solve these problems using iterative methods which are time‐consuming and prone to errors. For linear problems, basic method was found highly accurate and computationally sound. We derived a modified version of LFVIM to investigate and obtain the nondifferentiable solutions of linear, nonlinear, and nonhomogeneous LFPDEs arising in fractal vehicular traffic flow through illustrative examples. Study results show that both schemes are very effective and can be used successfully to solve fractal vehicular traffic flow problems.
In this paper, we prove the-convergence of a modified proximal point algorithm for common fixed points in a CAT(0) space for different classes of generalized nonexpansive mappings including a total asymptotically nonexpansive mapping, a multivalued mapping, and a minimizer of a convex function. The results in this paper generalize the corresponding results given by some authors. Moreover, numerical example is given to illustrate and show the-convergence of the proposed algorithm for supporting our result.
Buses are one of the important parts of public transport system. To provide accurate information about bus arrival and departure times at bus stops is one of the main parameters of good quality public transport. Accurate arrival and departure times information is important for a public transport mode since it enhances ridership as well as satisfaction of travelers. With accurate arrival-time and departure time information, travelers can make informed decisions about their journey. The application of artificial intelligence (AI) based methods/algorithms to predict the bus arrival time (BAT) is reviewed in detail. Systematic survey of existing research conducted by various researchers by applying the different branches of AI has been done. Prediction models have been segregated and are accumulated under respective branches of AI. Thorough discussion is presented to elaborate different branches of AI that have been applied for several aspects of BAT prediction. Research gaps and possible future directions for further research work are summarized.
In this paper, a hybrid iterative algorithm is proposed for finding a common element of the set of common fixed points of finite family of nonexpansive mappings and the set of common solutions of the variational inequality for an inverse strongly monotone mapping on the real Hilbert space. We establish the strong convergence of the proposed method for approximating a common element of the above defined sets under some suitable conditions. The results presented in this paper extend and improve some well-known corresponding results in the earlier and recent literature.
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