相关论文: A generalized Gronwall Inequality for Caputo Fract…
In many mathematical types of research, in order to solve the fuzzy fractional differential equations, we should transform these problems into crisp corresponding problems and by solving them the approximate solution can be obtained. The…
This short study consists of two parts, firstly we obtain some inequalities on Caputo Fractional derivatives using the elementary inequalities. Secondly we establish several new inequalities including Caputo fractional derivatives for…
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace…
In this paper, we consider the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and fractional vertical thermal diffusion. Global existence of classical solutions is established when the dissipation…
In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order $\alpha \in (0, 1)$. As initial data, we consider a pair consisting of an initial point, which does not…
In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $\alpha\in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $\alpha$. I also present a study about the…
This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems…
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some…
The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…
We consider a singular fractional differential equation involving generalized Katugampola derivative and obtain the existence and uniqueness of its solution. A scheme for uniformly approximating solution is constructed by using Picard…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…
This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the…
In this paper, we are primarily concerned with the study of entire and analytical solutions of abstract degenerate (multi-term) fractional differential equations with Caputo time-fractional derivatives. We also analyze systems of such…
Recently, some authors have proved monotonicity results for delta and nabla fractional differences separately. In this article, we use dual identities relating delta and nabla fractional difference operators to prove shortly the…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…
While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new…
We set-up and solve the Cauchy problem for Schr\"odinger-type differential operators with generalized functions as coefficients, in particular, allowing for distributional coefficients in the principal part. Equations involving such kind of…