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Asymptotically uniform functions: a single hypothesis which solves two old problems
The asymptotic study of a time-dependent function ƒ as the solution of a differential equation often leads to the question of whether its derivative
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Effects of local thickness defects on the buckling of micro-beam
A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the...
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Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces Wm,p (Ω)
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical...
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Kolmogorov n-widths for linear dynamical systems
Kolmogorov n -widths and Hankel singular values are two commonly used concepts in model reduction. Here, we show that for the special case of linear...
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A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications
Variable-order (VO) fractional differential equations (FDEs) with a time ( t ), space ( x ) or other variables dependent order have been successfully...
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Determination of the Correct Range of Physical Parameters in the Approximate Analytical Solutions of Nonlinear Equations Using the Adomian Decomposition Method
Physical parameters in dimensionless form in the governing equations of real-life phenomena naturally occur. How to control them by determining their...
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Effects of size-dependent elasticity on stability of nanotweezers
It is well-recognized that the electromechanical response of a nanostructure is affected by its element size. In the present article, the size...
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Method of quasilinearization for a nonlocal singular boundary value problem in weighted spaces
This paper studies the existence and uniqueness of solutions for a nonlocal singular boundary value problem of second-order integro-differential...
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Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side
We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea...
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Initial time difference quasilinearization for Caputo Fractional Differential Equations
This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and...
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Power Series of Bernstein Operators and Approximation of Resolvents
According to the theory developed by F. Altomare and his school, certain C 0 -semigroups can be approximated by iterates of positive linear operators....
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Three-points interfacial quadrature for geometrical source terms on nonuniform grids
This paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent...
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Nonlinear boundary value problems for discontinuous delayed differential equations
In this paper nonlinear boundary value problems for discontinuous delayed differential equations are considered. Some existence and boundedness...
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Approximating solutions of neutral stochastic evolution equations with jumps
In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson...
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Approximate explicit solution of Camassa-Holm equation by He’s homotopy perturbation method
In this paper, the homotopy perturbation method (HPM) is employed to solve Camassa-Holm equation. Approximate explicit solution is obtained....
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Application of ATS in a Quantum-optical Model
The problem of the interaction of a single two-level atom with a single mode of the quantized electromagnetic field in a coherent state in an ideal...
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Adapted BDF Algorithms: Higher-order Methods and Their Stability
We present BDF type formulas of high-order (4, 5 and 6), capable of the exact integration (with only round-off errors) of differential equations...
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Power expansions for the self-similar solutions of the modified Sawada-Kotera equation
The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is...
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Symplectic structure of poisson system
When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function...