Related papers: A new study on the mild solution for impulsive fra…
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…
A program dedicated to the numerical solution of the evolution equations for twist-three multiparton correlation functions is presented. The solutions are obtained by direct integration on a discretized momentum fraction grid. Both flavor…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
In recent years, much attention has been paid to the study of forward and inverse problems for the Rayleigh-Stokes equation in connection with the importance of this equation for applications. This equation plays an important role, in…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As…
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…
A well-posedness result for a time-shift invariant class of evolutionary operator equations involving material laws with fractional time-integrals of order $\alpha\in]0,1[$ is considered and exemplified by an application to a Kelvin-Voigt…
In an abstract Banach space we study conditions for the existence of piecewise continuous, almost periodic solutions for semi-linear impulsive differential equation with fixed and non-fixed moments of impulsive action
We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of the semigroup approach with locally monotone coefficients. An important component of the proof is…
We develop proper correction formulas at the starting $k-1$ steps to restore the desired $k^{\rm th}$-order convergence rate of the $k$-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order…
We provide an existence and uniqueness result for mild solutions to rough partial differential equations in the framework of the semigroup approach. Applications to stochastic partial differential equations driven by infinite dimensional…
In this article we deal with the stability and convergence of numerical solutions of nonlinear evolution equations of the form $A(u(t))+f(u(t))=u'(t)$, the numerical analysis of solutions to this problems will be performed using some…
We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…
In this note, we study the non-linear evolution problem $dY_t = -A Y_t dt + B(Y_t) dX_t$, where $X$ is a $\gamma$-H\"older continuous function of the time parameter, with values in a distribution space, and $-A$ the generator of an…
We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a…