Related papers: General Fractional Integrals and Derivatives with …
For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in the works Mathematics 9(6) (2021) 594 and Symmetry 13(5) (2021) 755. In these works, the proposed approaches to formulate this calculus are…
In this paper, we give some results on closed polynomials and factorially closed polynomial in $n$ variables. In particular, we give a characterization of factorially closed polynomials in $n$ variables over an algebraically closed field…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The…
We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
In recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded)…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
In this article, we introduce a class of multilinear fractional integral operators with generalized kernels that are weaker than the Dini kernel condition. We establish the boundedness of multilinear fractional integral operators with…
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…
Several approaches to the formulation of a fractional theory of calculus of "variable order" have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
In this paper we study some local and global regularity properties of Fourier series obtained as fractional integrals of modular forms. In particular we characterize the differentiability at rational points, determine their H\"older…
We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier…
Definitions of fractional derivative of order $\alpha$ ($0 < \alpha \leq 1$) using non-singular kernels have been recently proposed. In this note we show that these definitions cannot be useful in modelling problems with a initial value…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…