Related papers: Differential equations in Ward's calculus
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\Gamma$…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
We introduce a \emph{q}-differential operator adapted to \emph{q}-spinor variables, establishing a corresponding \emph{q}-spinor chain rule and defining both standard and Dirac-type \emph{q}-differential operators. Integral formulas in…
In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. We motivate our approach by illustrative examples.
In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…
This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…
The aim of this work is to study the existence of a periodic solutions of nth-order differential equations with delay d dt x(t) + d 2 dt 2 x(t) + d 3 dt 3 x(t) + ... + d n dt n x(t) = Ax(t) + L(xt) + f (t). Our approach is based on the…
In this study , we display a generalization of Darbos fixed point theorem , by using the use of a freshly made contraction operator and that we use to study the solvability of an integral equation involving the weighted fractional integral…
Local indices at isolated fixed points of a differentiable compact nonlinear map $T$ on Banach spaces will be discussed. These results are applied to establish the existence of nontrivial solutions. As an example, the existence of…
The aim of this work is to study the existence of a periodic solutions of integro-differential equations d dt [x(t)-- L(x t)] = A[x(t)-- L(x t)]+ G(x t)+ t --$\infty$ a(t-- s)x(s)ds+ f (t), (0 $\le$ t $\le$ 2$\pi$) with the periodic…
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running…
We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We provide algorithms computing power series solutions of a large class of differential or $q$-differential equations or systems. Their number of arithmetic operations grows linearly with the precision, up to logarithmic terms.