Related papers: The first order partial differential equations res…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a…
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
Ordinary differential equations of the first order on the torus have been investigated in detail by H. Poincar\'e and A. Denjoy. The long-standing problem of generalising these results for the equations of the order $k>1$ (or for the…
The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using…
We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
In this paper, with the help of previously constructed self-similar solutions, a solution of the Cauchy problem for an equation of even order with a fractional Riemann-Liouville derivative of order $1<\alpha<2$ is obtained.
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We adopt a procedure of operational-umbral type to solve the $(1+1)$-dimensional fractional Fokker-Planck equation in which time fractional derivative of order $\alpha$ ($0 < \alpha < 1$) is in the Riemann-Liouville sense. The technique we…