PubMed İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650
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Article Citation - WoS: 38Citation - Scopus: 40Study of Impulsive Problems Under Mittag-Leffler Power Law(Elsevier Sci Ltd, 2020) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, ThabetThis article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome.Article Citation - WoS: 34Citation - Scopus: 43Study of Global Dynamics of Covid-19 Via a New Mathematical Model(Elsevier, 2020) Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; Din, Rahim UdThe theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.Article Citation - WoS: 86Qualitative Analysis of a Mathematical Model in the Time of Covid-19(Hindawi Ltd, 2020) Mahariq, Ibrahim; Jarad, Fahd; Shah, Kamal; Abdeljawad, ThabetIn this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.Article Citation - WoS: 44Citation - Scopus: 53On a New Conceptual Mathematical Model Dealing the Current Novel Coronavirus-19 Infectious Disease(Elsevier, 2020) Shah, Kamal; Seadawy, Aly; Alrabaiah, Hussam; Baleanu, Dumitru; Din, AnwarudThe present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.Article Citation - WoS: 37Citation - Scopus: 43Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method(Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, FahdIn this paper, we are concerned with finding numerical solutions to the class of time-space fractional partial differential equations: D(t)(p)u(t, x) + kappa D(x)(p)u(t, x) + tau u(t, x) = g(t, x), 1 < p < 2, (t, x) is an element of [0,1] x [0, 1], under the initial conditions. u(0, x) = theta(x), u(t)(0, x) = phi(x), and the mixed boundary conditions. u(t, 0) = u(x)(t, 0) = 0, where D-t(p) is the arbitrary derivative in Caputo sense of order p corresponding to the variable time t. Further, D-x(p) is the arbitrary derivative in Caputo sense with order p corresponding to the variable space x. Using shifted Jacobin polynomial basis and via some operational matrices of fractional order integration and differentiation, the considered problem is reduced to solve a system of linear equations. The used method doesn't need discretization. A test problem is presented in order to validate the method. Moreover, it is shown by some numerical tests that the suggested method is stable with respect to a small perturbation of the source data g(t, x). Further the exact and numerical solutions are compared via 3D graphs which shows that both the solutions coincides very well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.Article Citation - WoS: 81Citation - Scopus: 91Existence Theory and Numerical Solutions To Smoking Model Under Caputo-Fabrizio Fractional Derivative(Amer inst Physics, 2019) Shah, Kamal; Zaman, Gul; Jarad, Fahd; Khan, Sajjad AliIn this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab. Published under license by AIP Publishing.