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A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which…
A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…
This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher--KPP equations, stochastic Allen--Cahn,…
Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness…
We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques.
In this paper we study the effect of the subordination by a general random time-change to the solution of a model on spatial ecology in terms of its evolution density. In particular on traveling waves for a non-local spatial logistic…
We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with…
Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
In this paper, we propose a fractional time extension of the Quan tum Master Equation. We introduce a Caputo-type fractional derivative in time as an extension of the exponential decay of the Lindblad framework through the incorporation of…