Related papers: Modified approach for linear and non-linear IBVPs …
In this article we introduce an analytical method, namely Homotopy Analysis Transform Method (HATM) which is a combination of Homotopy Analysis Method (HAM) and Laplace Decomposition Method (LDM).This scheme is simple to apply linear and…
Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under…
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…
In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…
This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of $\Psi$-Hilfer hybrid fractional differential equations (FDEs) and boundary value problem (BVP) for a coupled…
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is particularly efficient when coupled with a recently-introduced…
We study existence, uniqueness and regularity of solutions for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal…
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…