Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 25Citation - Scopus: 23Existence and Uniqueness of Solutions for Fractional Nonlinear Hybrid Impulsive System(Wiley, 2022) Jarad, Fahd; Valliammal, Natarajan; Ravichandran, Chokkalingam; Nisar, Kottakkaran Sooppy; Gupta, VidushiThe investigation of existence and uniqueness of impulsive dynamical fractional systems with quadratic perturbation of second type subject to nonlocal boundary conditions is presented and proved. By employing the fractional theory, Banach contraction technique, and Krasnoselskii's fixed point theorem, we derived some sufficient conditions to ensure the existence of our system. An example is offered to enhance the applicability of the results obtained.Article Citation - WoS: 4Citation - Scopus: 3Approximate Solutions of Nonlinear Two-Dimensional Volterra Integral Equations(Wiley, 2021) Nawaz, Rashid; Akbar, Muhammad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ahsan, SumbalThe present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two-dimensional Volterra integral equations (2D-VIEs). The result obtained by the suggested method for linear 2D-VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block-plus method and result of the proposed method for nonlinear 2D-VIEs is compared with 2D differential transform method. The proposed method provides us with efficient and more accurate solutions compared to the other existing methods in the literature.Article Citation - WoS: 6Citation - Scopus: 9Structure Preserving Algorithms for Mathematical Model of Auto-Catalytic Glycolysis Chemical Reaction and Numerical Simulations(Springer Heidelberg, 2020) Ahmed, Nauman; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Khan, Ilyas; Ali, Mubasher; Nisar, Kottakkaran SooppyThis paper aims to develop positivity preserving splitting techniques for glycolysis reaction-diffusion chemical model. The positivity of state variables in the glycolysis model is an essential property that must be preserved for all choices of parameters. We propose two splitting methods that remain dynamically consistent with the continuous glycolysis reaction-diffusion model. The proposed methods converge to a true steady-state or fixed point under the given condition. On contrary to the classical operator splitting finite difference methods, we use nonstandard finite difference theory to propose a new class of operator splitting techniques.