Abdelhakim, Ahmed A.
Published in
Fractional Calculus and Applied Analysis

We point out a major flaw in the so-called conformable calculus. We demonstrate why it fails at defining a fractional order derivative and where exactly these tempting conformability properties come from.

Sin, Chung-Sik
Published in
Fractional Calculus and Applied Analysis

In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis tec...

Dubovski, Pavel B. Slepoi, Jeffrey
Published in
Fractional Calculus and Applied Analysis

We construct the existence theory for generalized fractional Bessel differential equations and find the solutions in the form of fractional or logarithmic fractional power series. We figure out the cases when the series solution is unique, non-unique, or does not exist. The uniqueness theorem in space Cp is proved for the corresponding initial valu...

Droghei, Riccardo
Published in
Fractional Calculus and Applied Analysis

In this paper we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving particular values to the parameters involved in this special function, this leads to some known special functio...

Kiryakova, Virginia
Published in
Fractional Calculus and Applied Analysis

Navascués, María Mohapatra, Ram N. Chand, Arya K.B.
Published in
Fractional Calculus and Applied Analysis

We consider the fractal convolution of two maps f and g defined on a real interval as a way of generating a new function by means of a suitable iterated function system linked to a partition of the interval. Based on this binary operation, we consider the left and right partial convolutions, and study their properties. Though the operation is not c...

Jiao, Caiyu Khaliq, Abdul Li, Changpin Wang, Hexiang
Published in
Fractional Calculus and Applied Analysis

In general, the Riesz derivative and the fractional Laplacian are equivalent on ℝ. But they generally are not equivalent with each other on any proper subset of ℝ. In this paper, we focus on the difference between them on the proper subset of ℝ.

González-Camus, Jorge Ponce, Rodrigo
Published in
Fractional Calculus and Applied Analysis

In this paper we introduce a discrete fractional resolvent family {Sα,βn}n∈N0 $\begin{array}{} \displaystyle \{S_{\alpha,\beta}^n\}_{n\in\mathbb{N}_0} \end{array}$ generated by a closed linear operator in a Banach space X for a given α, β > 0. Moreover, we study its main properties and, as a consequence, we obtain a method to study the existence an...

Mazza, Mariarosa
Published in
Fractional Calculus and Applied Analysis

Two of the most famous definitions of fractional derivatives are the Riemann-Liouville and the Caputo ones. In principle, these formulations are not equivalent and ask for different levels of regularity of the considered function. By focusing on a B-spline collocation discretization of both kind of derivatives, we show that when the fractional orde...

Zhang, Xuping Chen, Pengyu O’Regan, Donal
Published in
Fractional Calculus and Applied Analysis

In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic...