*Correspondence: [email protected] Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan, R.O.C. Abstract In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields of science and engineering. Many authors...

Fractional differential calculus have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory, and biophysics, etc. [1-4]. In particular, the existence of solutions to fractional boundary value problems is under strong research recently, see [5-7] and references therein. The fractional q-difference c...

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...

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...

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...

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...

Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two that much studied in the literature are Hadamard-type tempered calculus. This paper establishes a connection between these two definitions, writing one terms other by making use theory with respect functions. By extending this natural way, ...