Ulam-Hyers stability and analytical approach for m-dimensional Caputo space-time variable fractional order advection-dispersion equation

作     者：Pratibha Verma Manoj Kumar Anand Shukla 

作者机构：Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj–211004Uttar PradeshIndia†Department of Mathematics Wollega UniversityNekemteEthiopia 

出 版 物：《International Journal of Modeling, Simulation, and Scientific Computing》 (建模、仿真和科学计算国际期刊（英文）)

年 卷 期：2022年第13卷第1期

页      面：131-174页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Fixed point theorems space-time variable Caputo’s fractional operators advection-dispersion equation Ulam-Hyers stability two-step Adomian decomposition method 

摘      要：This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration.Moreover,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new results.Also,obtain the Ulam–Hyers stabilities for the proposed problem.Two gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical methods.The present method performs exceptionally well in terms of efficiency and simplicity.Further,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.