Search

The fractional advection–dispersion equation is used in groundwater hydrology for modeling the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. This model is used for the prediction of the transport of nonreactive dissolved contaminants in groundwater. This paper establishes the existence and the uniqueness of solutions represented as fractional bi-variate power series of some initial-value problems and boundary-value problems for the fractional advection–dispersion equation. Moreover, a method to approximate the solutions using fractional polynomials in two variables and to evaluate the errors in a suitable rectangle is designed. Illustrative examples showing the applicability of the theoretical results are presented. [ABSTRACT FROM AUTHOR]

The α -fractional power moduli series are introduced as a generalization of α -fractional power series and the structural properties of these series are investigated. Using the fractional Taylor's formula, sufficient conditions for a function to be represented as an α -fractional power moduli series are established. Beyond theoretical formulations, a practical method to represent solutions to boundary value problems for fractional differential equations as α -fractional power series is discussed. Finally, α -analytic functions on an open interval I are defined, and it is shown that a non-constant function is α -analytic on I if and only if 1 / α is a positive integer and the function is real analytic on I. [ABSTRACT FROM AUTHOR]

The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered subjected to the boundary conditions To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]).

Fractional Taylor series are studied. Then solutions of fractional linear ordinary differential equations (FODE), with respect to Caputo derivative, are approximated by fractional Taylor series. The Cauchy-Kowalevski theorem is proved to show the existence and uniqueness of local solutions for FODE with Cauchy initial data. Sufficient conditions for the global existence of the solution and the estimate of error are given for the method using fractional Taylor series. Two illustrative numerical examples are given to demonstrate the validity and applicability of this method.

This paper deals with the study of the solution of the problem modeling the motion of a SDOF semiactive base isolation systems with controllable dry friction, proportional with absolute value of relative displacement. The method are based on a representation of the solution as a piecewise analytic function. The transmissibility factors of considered systems, defined in terms of r.m.s. values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. [ABSTRACT FROM AUTHOR]

A representation of strictly convergent power series as Newton interpolating series is given. In the case of one indeterminate bounded Newton interpolating series are studied as a generalization of strictly convergent power series. A method for analytic p-adic continuation by means of bounded Newton interpolating series is presented. [ABSTRACT FROM AUTHOR]

A real Banach algebra of Newton interpolating series, used to approximate the solutions of multipoint boundary value problems for ODE's, is studied. [ABSTRACT FROM AUTHOR]

If K is a field with a non-trivial non-Archimedean absolute value (multiplicative norm) | |, we describe all non-Archimedean K-algebra norms on the polynomial algebra K[X1, …,Xr] which extend | |. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, and let | | be a non-trivial absolute value on R. We study the R-algebra norms on the polynomial algebra R[ X 1, ... , X r ] which extend | |. [ABSTRACT FROM AUTHOR]