The Mittag-Leffler Function for Re-Evaluating the Chlorine Transport Model: Comparative Analysis

被引:9
作者
Aljohani, Abdulrahman F. [1 ]
Ebaid, Abdelhalim [1 ]
Algehyne, Ebrahem A. [1 ]
Mahrous, Yussri M. [2 ]
Cattani, Carlo [3 ]
Al-Jeaid, Hind K. [4 ]
机构
[1] Univ Tabuk, Fac Sci, Dept Math, Computat & Analyt Math & Their Applicat Res Grp, Tabuk 71491, Saudi Arabia
[2] Univ Tabuk, Fac Community, Dept Studies & Basic Sci, Tabuk 71491, Saudi Arabia
[3] Univ Tuscia, Engn Sch DEIM, I-01100 Viterbo, Italy
[4] Umm Al Qura Univ, Dept Math Sci, Mecca 21955, Saudi Arabia
关键词
fractional partial differential equation; Mittag-Leffler function; boundary value problem; separation of variables; Laplace transform; CONCENTRATION DECAY; SERIES SOLUTION; WATER; INACTIVATION;
D O I
10.3390/fractalfract6030125
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper re-investigates the mathematical transport model of chlorine used as a water treatment model, when a variable order partial derivative is incorporated for describing the chlorine transport system. This model was introduced in the literature and governed by a fractional partial differential equation (FPDE) with prescribed boundary conditions. The obtained solution in the literature was based on implementing the Laplace transform (LT) combined with the method of residues and expressed in terms of regular exponential functions. However, the present analysis avoids such a method of residues, and thus a new analytical solution is introduced in this paper via Mittag-Leffler functions. Therefore, an effective approach is developed in this paper to solve the chlorine transport model with non-integer order derivative. In addition, our results are compared with several studies in the literature in case of integer-order derivative and the differences in results are explained.
引用
收藏
页数:14
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