Browsing by Author "Kumar, S."

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A New Class of Contraction in b -Metric Spaces and Applications
(2017) Kaushik, P.; Kumar, S.; Kenan, Taş
A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. © 2017 Preeti Kaushik et al.
Citation - Scopus: 14
A Fractional Order Co-Infection Model Between Malaria and Filariasis Epidemic
(Taylor and Francis Ltd., 2024) Kumar, A.; Kumar, S.; Baleanu, D.; Kumar, P.
In this article, we investigate a mathematical malaria-filariasis co-infection model with the assistance of the non-integer order operator. Using the fractal-fractional operator in the Caputo-Fabrizio (CF) sense, it has been possible to understand the dynamical behaviour and complicatedness of the malaria-filariasis model. An investigation of the existence and uniqueness of the solution employs fixed-point theory. Ulam-Hyers stability helps examine the stability analysis of the proposed co-infection model. The malaria-filariasis model has been investigated using the Toufik-Atanagana (TA), a sophisticated numerical method for these biological co-infection models. With the help of numerical procedures, we provide the approximate solutions for the proposed model. A variety of fractal dimension and fractional order options are utilized for the presentation of the results. When we adjust sensitive parameters like τ and γ, the graphical representation illustrates the system’s behaviour and identifies suitable parameter ranges for solutions. In addition, we evaluate the model along with the regarded operators and various β1 values using an exceptional graphical representation. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
Introduction To the Special Issue on Mathematical Aspects of Computational Biology and Bioinformatics-II
(Tech Science Press, 2025) Baleanu, D.; Pinto, C.M.A.; Kumar, S.
Citation - Scopus: 5
A New Class of Contraction in B -Metric Spaces and Applications
(Hindawi Limited, 2017) Kumar, S.; Tas, K.; Kaushik, P.
A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. © 2017 Preeti Kaushik et al.
Variational Iteration Method for Generalized Pantograph Equation With Convergence Analysis
(L and H Scientific Publishing, LLC, 2014) Baleanu, D.; Karimi, K.; Kumar, S.; Alipour, M.
In this paper, we solve generalized pantograph equation by changing the problem to a system of ordinary equations and using the variational iteration method. We discuss convergence of the proposed method to the exact solution. Finally, illustrative examples are given to demonstrate the efficiency of the method. © 2014 L and H Scientific Publishing, LLC.