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 ...

This paper investigates a class of sharp integral means inequalities involving fractional calculus operators of certain analytic functions with negative coefficients. Some consequences of the main result are also mentioned.

This paper introduces a new fractional operator by using the concepts of q-calculus and q-Mittag-Leffler functions. With this operator, Janowski functions are generalized studied regarding their certain geometric characteristics. It also establishes solution complex Briot–Bouquet differential equation newly defined operator.

Abstract In this paper, we give some basic concepts of q -calculus that will be needed in paper. Then, built the q-nonlocal condition ensures solution existence and uniqueness fractional q-integrodifferential equation. Also, introduce continuous dependence solution. We find numerical using finite-difference-Trapezoidal cubic B-spline-Trapezoidal methods. Finally, three examples to illustrate va...

*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...

We introduce the concept of q-calculus in quantum geometry. This involves q-differential and q-integral operators. With these, we study basic rules governing as compared with classical Newton-Leibnitz calculus, obtain some important results. reduced transform method (RqDTM) for solving partial equations. The solution is computed form a convergent power series easily computable coefficients. hel...