Browsing by Author "Kumar, Anoop"

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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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    A mathematical study of a tuberculosis model with fractional derivatives
    (World Scientific, 2021-02-04T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Erturk, Vedat Suat; Kumar, Anoop
    In this work, we use a Predictor-Corrector method to implement and derive an iterative solution of an existing Tuberculosis (TB) model with two fractional derivatives, namely, Caputo-Fabrizio fractional derivative and the new generalized Caputo fractional derivative. We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model. Then, we study the global asymptotic stability of disease-free equilibrium of the fractional models. We also prove, for each fractional model, the existence and uniqueness of solutions. An iterative solution of the two models is computed using the Predictor-Corrector method. Using realistic parameter values, we perform numerical simulations for different values of the fractional order. Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo-Fabrizio fractional derivative and the classical integer-order TB model. � 2021 World Scientific Publishing Company.
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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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    Prediction studies of the epidemic peak of coronavirus disease in Japan: From Caputo derivatives to Atangana-Baleanu derivatives
    (World Scientific, 2021-09-30T00:00:00) Kumar, Pushpendra; Rangaig, Norodin A.; Abboubakar, Hamadjam; Kumar, Anoop; Manickam, A.
    New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo-Fabrizio derivatives, and Atangana-Baleanu derivatives in the Caputo sense. The fixed point theory and Picard-Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order ?, and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals. � 2022 World Scientific Publishing Company.
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    Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon
    (Elsevier Ltd, 2021-06-21T00:00:00) Abboubakar, Hamadjam; Kombou, Lausaire Kemayou; Koko, Adamou Dang; Fouda, Henri Paul Ekobena; Kumar, Anoop
    In this work, we formulate a mathematical model with a non-integer order derivative to investigate typhoid fever transmission dynamics. To combat the spread of this disease in the human community, control measures like vaccination are included in the proposed model. We calculate the epidemiological threshold called the control reproduction number, Rc, and perform the asymptotic stability of the typhoid-free equilibrium point. We prove that the typhoid-free equilibrium for both integer and non-integer models is locally and globally asymptotically stable whenever Rc is less than one. We also prove that both models admit only one endemic equilibrium point which is globally asymptotically stable whenever Rc>1 and no endemic equilibrium point otherwise. This means that the backward bifurcation phenomenon does not occur. In absence of vaccination, Rc is equal to the basic reproduction number R0. We found out that Rc1), and then to predict new cases of typhoid fever per month at Mbandjock in the next new year. To determine model parameters that are responsible for disease spread in the human community, we perform sensitivity analysis (SA). This analysis shows that the vaccination rate, the human-bacteria contact rate, as well as the recovery rate, are the most important parameters in the disease spread. To validate our analytical results, and to see the impact of some control measures in the spread of typhoid fever in the human community, as well as the impact of the fractional-order on typhoid transmission dynamics, we perform several numerical simulations. � 2021 Elsevier Ltd
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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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    A study on controllability for Hilfer fractional differential equations with impulsive delay conditions
    (American Institute of Mathematical Sciences, 2022-12-05T00:00:00) Karthikeyan, Kulandhaivel; Sekar, Palanisamy Raja; Karthikeyan, Panjaiyan; Kumar, Anoop; Botmart, Thongchai; Weera, Wajaree
    This article focuses on the controllability of a Hilfer fractional impulsive differential equation with indefinite delay. We analyze our major outcomes using fractional calculus, the measure of non-compactness and a fixed-point approach. Finally, an example is provided to show the theory. � 2023 the Author(s), licensee AIMS Press.