in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution p...

Abstract. 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 discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .

In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties polynomials are obtained including generating functions, finite sums, and Laplace integral transforms. addition, further investigated using fractional calculus operators.

Abstract In this paper, we first provide a short summary of the main properties so-called general fractional derivatives with Sonin kernels introduced so far. These are integro-differential operators defined as compositions order derivative and an integral operator convolution type. Depending on succession these operators, Riemann-Liouville Caputo types were studied. The objective paper is cons...

This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior of a manifold with boundary, where the boundary has the structure of a tower of fibre bundles. The class of operators we consider on such a space includes th...

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

A many variable q-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The special cases of two dimensional supersymmetry and fractional supersymmetry are developed in detail. PACS 02.10T, 11.30P, 03.65F. e-mail: [email protected]...

An extension of the general fractional calculus (GFC) is proposed as a generalization Riesz calculus, which was suggested by Marsel in 1949. The form GFC can be considered an from positive real line and Laplace convolution to m-dimensional Euclidean space Fourier convolution. To formulate form, Luchko approach construction GFC, Yuri 2021, used. integrals derivatives are defined convolution-type...

In this paper, a generalization of the q-Meyer-K?nig and Zeller operators by means (p,q)- calculus is introduced. Some approximation results for (p,q)-analogue Meyer-K?nig denoted Mn,p,q 0 < q p ? 1 are obtained. Also we investigate classical statistical versions Korovkin type based on proposed operator. Furthermore, some graphical examples convergence presented.