• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.597-620
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• 2024

In this study, the conformable fractional derivative(CFD) of order 𝝔 in conjunction with the LC operator of orderρ is used to develop the model of the transmission of the A(H1N1) influenza infection. A brand-new A(H1N1) influenza infection model is presented, with a population split into four different compartments. Fixed point theorems were used to prove the existence of the solutions and uniqueness of this model. The basic reproduction number R₀ was determined. The least and most sensitive variables that could alter R₀ were then determined using normalized forward sensitivity indices. Through numerical simulations carried out with the aid of the Adams-Moulton approach, the study also investigated the effects of numerous biological characteristics on the system. The findings demonstrated that if 𝝔 < 1 and ρ < 1 under the CFD, also the findings demonstrated that if 𝝔 = 1 and ρ = 1 under the CFD, the A(H1N1) influenza infection will not vanish.

• Ocean Systems Engineering
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• v.4 no.2
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• pp.83-97
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• 2014

Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.