Related papers: Precise interpretation of the conformable fraction…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
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 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…
In this paper, Newton's law of cooling is considered from a different perspective with newly defined fractional conformable. Obtained results are compared with experimental results and found optimal fractional orders which fit better with…
Historically the fractional calculus concept works an extended idea based on the question asked by Guillaume de L'H\^opital to Gottfried Wilhelm Leibniz in 1695 about the notation ${d^nf}/{dx^n}$ for the derivative operator "What if…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…
A new calculus on fractal curves, such as the von Koch curve, is formulated. We define a Riemann-like integral along a fractal curve F, called F-alpha-integral, where alpha is the dimension of F. A derivative along the fractal curve called…
It is well known that for every $f\in C^m$ there exists a polynomial $p_n$ such that $p^{(k)}_n\rightarrow f^{(k)}$, $k=0,\ldots,m$. Here we prove such a result for fractional (non-integer) derivatives. Moreover, a numerical method is…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
In this paper, we propose a new fractional derivative, which is based on a Caputo-type derivative with a smooth kernel. We show that the proposed fractional derivative reduces to the classical derivative and has a smoothing effect which is…
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem,…
The aim of this paper is to obtain the existence of solutions for the following fractional p-Laplacian Dirichlet problem with mixed derivatives \begin{eqnarray*}…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and 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…