Department Of Mathematics And Statistics

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Browsing Department Of Mathematics And Statistics by Author "Abdeljawad, Thabet"

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    Existence of solutions by fixed point theorem of general delay fractional differential equation with p-Laplacian operator
    (American Institute of Mathematical Sciences, 2023-02-27T00:00:00) Kaushik, Kirti; Kumar, Anoop; Khan, Aziz; Abdeljawad, Thabet
    In this manuscript, the main objective is to analyze the existence, uniqueness,(EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing ?p-Laplacian operator. To continue, we will apply Green�s function to determine the suggested FDE�s equivalent integral form. The Guo-Krasnosel�skii fixed point theorem and the properties of the p-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result. � 2023 the Author(s), licensee AIMS Press.
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    Mild solutions of coupled hybrid fractional order system with caputo-hadamard derivatives
    (World Scientific, 2021-05-15T00:00:00) Bedi, Pallavi; Kumar, Anoop; Abdeljawad, Thabet; Khan, Aziz; G�mez-Aguilar, J.F.
    This paper is devoted to prove the existence of mild solutions of coupled hybrid fractional order system with Caputo-Hadamard derivatives using Dhage fixed point theorem in Banach algebras. In order to confirm the applicability of obtained result an example is also presented. � 2021 World Scientific Publishing Company.
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    Stability analysis of neutral delay fractional differential equations with Erdelyi�Kober fractional integral boundary conditions
    (Elsevier B.V., 2023-08-11T00:00:00) Bedi, Pallavi; Kumar, Anoop; Khan, Aziz; Abdeljawad, Thabet
    The primary focus of this article is to provide sufficient conditions for the Ulam�Hyers stability of neutral delay fractional differential equations involving Hilfer fractional derivatives and Erdelyi�Kober fractional integral boundary conditions. The fixed point approach is utilized to prove the existence and uniqueness of mild solutions for the proposed problem. In the end, the derived results are validated through an illustrative example. � 2023 The Author(s)
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    Transmission dynamics of a novel fractional model for the Marburg virus and recommended actions
    (Springer Science and Business Media Deutschland GmbH, 2023-08-02T00:00:00) Singh, Jaskirat Pal; Abdeljawad, Thabet; Baleanu, Dumitru; Kumar, Sachin
    Marburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana�Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R< 1 , Castillo�s method and the next-generation matrix are used to demonstrate the disease-free equilibrium�s asymptotic global stability. When R> 1 , the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model�s basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution�s existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model�s numerical simulations. � 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.