This research study focuses on the analytical behavior and numerical computation of the fractional order Ebola model. In this study we have calculated the conditions for the existence, uniqueness, and stability of the solution with the help of the fixed point results. In addition to this, we calculated the numerical solution of the fractional order smoke model with the help two‐step fractional Adam’s Bashforth method using the Caputo’s fractional derivative of order μ . Furthermore, the results obtained for different orders of the fractional derivative μ have been shown graphically with the help of Matlab.
A mosquito born viral disease (Dengue) becoming endemic around the globe which including cause of severe illness and death in various Asian and Latin American countries. It needs proper management by researchers and medicine professionals. The current research work is a step towards the prevention/reduction of such deadly disease in the society. More precisely, this work addressing various mathematical proofs interconnected to the existence and stability along with numerical findings by using mathematical modeling techniques. Further, the existence results have been established for the proposed model under the Atangana-Baleanu derivative in Caputo sense (ABC) with fractional order. In continuation, we find the deterministic stability for the proposed model. Lastly, the new version of numerical approximation's framework for the approximation of ABC fractional derivative is used to carried out the numerical simulation for the obtained results.
Let G be a connected graph then ܰ-index (݇-distance degree index) defined in [14] as ܰ(ܩ)=∑ௗ(ீ)ୀଵቀ∑௫ఢ(ீ)݀(ݔ)ቁ݇, where ݀(ݔ)=|ܰ(ݔ)|=|{ݕܸ߳(ܩ):݀(ݔ,ݕ)=݇}|, where ݀(ݔ,ݕ)is the distance between vertex ݔand ݕin graph ܩand ݉ܽ݅݀(ܩ)is the diameter of graph ܩ. We define some transformations and their impact on ܰ-index of graphs with respect to pendant path and pendant vertices. For fixed number of pendant vertices of a tree, we define a tree with minimum ܰ-index. Also for different fixed parameters we characterize the tress with minimum ܰ-index.
In this article, the qualitative theory and approximate solutions for fractional order Ebola model via Atangana-Baleanu-Caputo (ABC) fractional operators are developed. Using various tools of analysis, the conditions for the existence and stability of the proposed model are established. With the help of Laplace Adomain Decomposition method, we obtain the approximate solutions for the said model. In the last part, using Matlab, we plotted various graphs to discuss the underlying model for different fractional order values of γ.
Adjusting of species with the rapid change that occurs in the conditions of various ecosystems and environment behavior are not easy for them with the passage of time. One can expect species fight against these forces to get rid of extinction, i.e., species tend to adapt genetically or move to a new environment to resilience against extinction. In this paper, a climate change model is investigated by Caputo fractional derivative. Firstly, the qualitative analysis of the solution of the fractional Climate Change model is found by the application of the theory of fixed point. For approximate solution, the iterative numerical techniques of the consider problem under Caputo derivative is presented. In the last part, the numerical approximation of plotting are provided for validation of our fractional-order iterative scheme. As a whole, the total spectrum lying between two integer values are achieved with more information about the complexity of the dynamics of the proposed fractional Climate Change-model.
The Zika virus is considered to be one of the dangerous virus, which spread in the community through small insect so-called mosquitoes. Some of the other will known methods by which the consider virus may transform are: pregnant mother can pass it to her baby during the pregnancy or birth time, it can also spread through sexual intercourse. Therefore, the world health organization (WHO) declares the Zika infection with clusters of microcephaly and other neurological disorders constitutes a public health emergency of international concern. To understand the dynamics of Zika infectious virus, we investigate the fractional order mathematical model for the transference of Zika infectious disease. The proposed model is divided into seven compartments. Particularly, the author's used the results of fixed point theory to discuss the existence and uniqueness of the solution and stability analysis for the proposed model. Furthermore, we have calculated the equilibrium points, basic reproduction number and stability of the basic reproduction number. In addition, for the numerical solution of the said model, the author's used two steps fractional Adam's Bashforth method (FABm). Finally, numerical simulation and discussion of the graphical representation of the solutions obtained via FABm are given.
The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having different orders are adjacent provided that o(a) divides o(b) or o(b) divides o(a).
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