The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators. We also provide simple closed forms for the ...

In this paper, we describe recent improvements to the theory of differentiation that is formalized in ACL2(r). First, we show how the normal rules for the differentiation of composite functions can be introduced in ACL2(r). More important, we show how the application of these rules can be largely automated, so that ACL2(r) can automatically define the derivative of a function that is built from...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

Background: Patients need peace of mind to disclose their information to medical staff and with the lack of trust or in specific health status, they may avoid providing sensitive information for their care or might change the information. This research aims to examine the impact of perceived health status and trust propensity on privacy calculus. Methods: This research was analytical-study. 3 ...

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...

We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this ZX diagrams, we show how calculate diagrammatically gradient of a linear map with respect phase parameter. For diagrams parametrised quantum circuits, get well-known parameter-shift rule at basis many variational algorithms. then extend our m...

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differentia...

Integration is the 'inverse of differentiation' is what we are told in our beginning calculus course. It is indeed the case when the given function is continuousl. Augustin Cauchy2 (1789 1857), a famous mathematician, was the first person to establish that any continuous function is the derivative of a differentiable function. The proof of this result, known as the Fundamental theorem of Calcul...