Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

نویسندگان

  • Rubayyi T. Alqahtani
  • R. T. Alqahtani
چکیده

The power law has been used to construct the derivative with fractional order in Caputo and RiemannLiouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater flowing within an unconfined aquifer. c ©2016 All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

متن کامل

Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives

The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana-Baleanu fractional derivative. Since the new Atangana-Baleanu fractional derivative is non-singular and non-local, the Euler-Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are sho...

متن کامل

An extension of stochastic differential models by using the Grunwald-Letnikov fractional derivative

Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach b...

متن کامل

Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer

and Applied Analysis 3 3. Numerical Solution Environmental phenomena, such as groundwater flow described by variational order derivative, are highly complex phenomena, which do not lend themselves readily to analysis of analytical models. The discussion presented in this section will therefore be devoted to the derivation of numerical solution to the modified Hantush equation (6). Solving diffi...

متن کامل

MODELING OF GROUNDWATER FLOW OVER SLOPING BEDS IN RESPONSE TO CONSTANT RECHARGE AND STREAM OF VARYING WATER LEVEL

This paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. The aquifer is in contact with a constant water level at one end. The other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. Moreover, the aquifer is repleni...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016