Related papers: A matrix method based on the Fibonacci polynomials…
We derive a collection of identities for bivariate Fibonacci and Lucas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables $x$ and $y$ are replaced by polynomials. A wealth of…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…
In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequence of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
We provide fundamental results on positive solutions to parametrized systems of generalized polynomial $\textit{inequalities}$ (with real exponents and positive parameters), including generalized polynomial $\textit{equations}$. In doing…
The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
In this work, we determine the general solution of the quinquevigintic functional equation and also investigate its stability of this equation in the setting of matrix normed spaces and the framework of matrix non-Archimedean fuzzy normed…
We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies.…
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the…
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients.…