Related papers: Substitution Method for Fractional Differential Eq…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type Fractional Derivative, and describe this method developed by us, to find out Particular Integrals,…
In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we…