The main objective of this paper is to formulate an epidemiological model using fractional order derivatives which has an advantage over the classical integer order models due to its memory effect property. Our mathematical formulation of the non-integer order initial value problem will be based on the famous fractional order Caputo derivative. We discuss and show the existence of non-negative solutions of the mathematical model. We further investigate local asymptotic stability analysis of model equilibria. Finally, numerical solutions are presented using Adams-type predictor-corrector method to illustrate fractional model trajectories.
In this paper we have constructed Randers, Kropina and Matsumoto space of order-k and their L-duals respectively, using the concepts of higher order(order k) Riemmanian, Finsler, Lagrangian structures and Legendre transformation.
The Burr Type III distribution attracts special attention in life testing and reliability analysis as it is applied in several areas such as economics and environmetrics among others. A composite distribution of Kumaraswamy and Burr Type III distributions, referred to as Kumaraswamy-Burr Type III distribution, is introduced and studied. It contains some special well-known distributions, which are discussed in lifetime literature, such as the Burr Type III, exponentiated Burr Type III and Kumaraswamy-Burr Type XII, among several others. Some properties of the proposed distribution are studied including explicit expressions for the moments, the density functions of the order statistics, Rényi entropy, quantiles and moment generating function. The method of maximum likelihood is applied under Type II censored samples for estimating the model parameters, reliability and hazard rate functions. For different values of sample sizes, Monte Carlo simulation is performed to investigate the precision of the maximum likelihood estimates.
In this paper, a bounded rational monopolist Bertrand model is proposed using a specific demand function. Therefore, some stability analysis is carried out to describe some complex dynamic phenomena such as bifurcation and chaos. Also, an approach for risk in the model which based on multi-objective method is studied.
Timetabling is a problem faced in all higher education institutions. The International Timetabling Competition (ITC) has published a dataset that can be used to test the quality of methods used to solve this problem. A number of meta-heuristic approaches have obtained good results when tested on the ITC dataset, however few have used the ant colony optimization technique, particularly on the ITC 2007 curriculum based university course timetabling problem. This study describes an ant system that solves the curriculum based university course timetabling problem and the quality of the algorithm is tested on the ITC 2007 dataset. The ant system was able to find feasible solutions in all instances of the dataset and close to optimal solutions in some instances. The ant system performs better than some published approaches, however results obtained are not as good as those obtained by the best published approaches. This study may be used as a benchmark for ant based algorithms that solve the curriculum based university course timetabling problem.
A semigraph G is vertex-labeled semigraph, if its n-vertices are labeled by distinct symbols. In this paper various results on enumeration of vertex-labeled semigraphs containing non-adjacent edges and number of vertex-labeled semigraphs with two adjacent s-edges are obtained. Also the number of vertex-labeled semigraphs on 1 to 8 vertices is calculated.