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Browsing by Author "Arshad, S."

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    Article
    Citation - WoS: 67
    Citation - Scopus: 74
    Dynamical Behaviours and Stability Analysis of a Generalized Fractional Model With a Real Case Study
    (Elsevier, 2023) Baleanu, D.; Arshad, S.; Jajarmi, A.; Shokat, W.; Ghassabzade, F. Akhavan; Wali, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    Introduction: Mathematical modelling is a rapidly expanding field that offers new and interesting oppor-tunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. Objectives: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework.Methods: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time -varying transmission rate, and consists of ten population classes including susceptible, infected, diag-nosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical beha-viours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated.Results: Numerical simulations are reported for various fractional orders, and simulation results are com-pared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied.Conclusion: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.& COPY; 2023 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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    Book Part
    Citation - Scopus: 13
    Fractional Differential Equations With Bio-Medical Applications
    (De Gruyter, 2019) Baleanu, D.; Tang, Y.; Arshad, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
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    Conference Object
    Citation - Scopus: 2
    Stability Analysis of Covid-19 Via a Fractional Order Mathematical Model
    (Springer Science and Business Media Deutschland GmbH, 2022) Defterli, O.; Baleanu, D.; Arshad, S.; Wali, M.; 56389; 31401; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this work, a four compartmental SEIR model is constructed for the transmission of the Novel Coronavirus infectious disease using Caputo fractional derivative. The disease-free equilibrium and endemic equilibrium are investigated with the stability analysis correspondingly. The solution at different fractional orders is obtained using the Laplace Adomian Decomposition method. Furthermore, the dynamics of the proposed fractional order model are interpreted graphically to observe the behaviour of the spread of disease by altering the values of initially exposed individuals and transmission rate. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.