相关论文: Application of fuzzy Laplace transforms for solvin…
The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gauss-type quadrature formula is used to approximate integrals during the…
A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci.,…
This article presents a novel solution method for nonautonomous linear ordinary fractional differential equations. The approach is based on reformulating the analytical solution using the $\star$-product, a generalization of the Volterra…
Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic…
In this work we present new methods for transforming and solving finite series by using the Laplace transform. In addition we introduce both an alternative method based on the Fourier transform and a simplified approach. The latter allows a…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
This paper addresses a new class of generalized Bolza problems governed by nonconvex integro-differential inclusions with endpoint constraints on trajectories, where the integral terms are given in the general (with time-dependent…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
In this paper, Belousov-Zhabotinsky (B-Z) reaction model with Caputo fractional time derivative is investigated by the fractional reduced differential transform method (FRDTM) methods, an iterative technique. The outcome using FRDTM method…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials…
In this paper we characterise the Lp stability of perturbed linear Volterra integrodifferential convolution equations. Additionally we provide a framework which points to necessary and sufficient conditions on the forcing function that…
One of the major challenges of contemporary mathematics is numerical solving of various problems for functional differential equations (FDE), in particular Cauchy problem for delayed and neutral differential equations. Recently large…
Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes, which require knowledge about the appearing…
We study the numerical solution for Volerra integro-differential equations with smooth and non-smooth kernels. We use a $h$-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of…
We consider a linear inhomogeneous fractional evolution equation which is obtained from a Cauchy problem by replacing its first-order time derivative with Caputo's fractional derivative. The operator in the fractional evolution equation is…