Related papers: Fractional derivative in spaces of continuous func…
This article deals with the regularity of the entropy solutions of scalar conservation laws with discontinuous flux. It is well-known [Adimurthi et al., Comm. Pure Appl. Math. 2011] that the entropy solution for such equation does not admit…
This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…
In this work, we establish the maximal $\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time. These schemes include…
The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
In this Short Note we complement the intriguing harmonic analytic perspective due to P. Auscher and A. Axelsson for the abstract evolution equations. This concerns a unified approach to temporally weighted estimates for the forward and…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
This paper deals with the embedding of the Sobolev spaces of fractional order into the space of H\"older continuous functions. More precisely, we show that the function $f\in H^s(\mathbb{R})$ with $\frac{1}{2}<s<1$ is H\"older continuous…
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…
The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fractional calculus of variations with free end-points are…
For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the…
I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition…
In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in Ayache, Roueff and Xiao (2007). By using this representation, in the case where the sample…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…