相关论文: On solution of Diffusion Equation using Conformabl…
It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…
In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of…
The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain $D$ of $ \mathbb{R}^{k}$, $k\ge 1$, which includes the fractional power $\mathcal L^\beta$, $0<\beta\le…
We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the…
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…
In this paper a novel contour integral method is proposed for linear convection-diffusion equations. The method is based on the inversion of the Laplace transform and makes use of a contour given by an elliptic arc joined symmetrically to…
We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…