相关论文: On the $\mathbf{\rm\Psi}-$fractional integral and …
We study the distribution of values of the Riemann zeta function $\zeta(s)$ on vertical lines $\Re s + i \mathbb{R}$, by using the theory of Hilbert space. We show among other things, that, $\zeta(s)$ has a Fourier expansion in the…
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…
Using the concept of fractional derivatives of Riemann$-$Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain…
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…
Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the…
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus…
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…
In this work we study the Riemann-Liouville fractional integral of order $\alpha\in(0,1/p)$ as an operator from $L^p(I;X)$ into $L^{q}(I;X)$, with $1\leq q\leq p/(1-p\alpha)$, whether $I=[t_0,t_1]$ or $I=[t_0,\infty)$ and $X$ is a Banach…
This paper is dedicated to $L^p$ bounds on eigenfunctions of a Sch\"odinger-type operator $(-\Delta_g)^{\alpha/2} +V$ on closed Riemannian manifolds for critically singular potentials $V$. The operator $(-\Delta_g)^{\alpha/2}$ is defined…
In this paper, we introduce a new generalized class of analytic functions involving the Mittag-Leffler operator and Bazilevi\u{c} functions. We examine inclusion properties, radius problems and an application of the generalized…
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the…
We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant…
Based on the fractional $q$-integral with the parametric lower limit of integration, we define fractional $q$-derivative of Riemann-Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we…
In this paper, we propose a solution of fractional logistic equation by using properties of Mittag-Leffler function.
In this paper, we extend the Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new integral inequalities for convex functions.
The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
In this paper we deduce a formula for the fractional Laplace operator $(-\Delta)^{s}$ on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with $(-\Delta)^{s}$, and apply it to a…