A study on fractional differential equations using the fractional Fourier transform

被引：0
|
作者：
Porpattama Hammachukiattikul
Arusamy Mohanapriya
Anumanthappa Ganesh
Grienggrai Rajchakit
Vediyappan Govindan
Nallappan Gunasekaran
Chee Peng Lim
机构：
[1] Phuket Rajabhat University,Department of Mathematics
[2] Adhiyamaan College of Engineering,Department of Mathematics
[3] Periyar University,Department of Mathematics, Government Arts and science College
[4] Maejo University,Department of Mathematics, Faculty of Science
[5] Sri Vidya Mandir Arts & Science College,Department of Mathematics
[6] Shibaura Institute of Technology,Department of Mathematical Sciences
[7] Deakin University,Institute for Intelligent Systems Research and Innovation
来源：
Advances in Difference Equations | / 2020卷
关键词：
Hyers–Ulam–Rassias stability; Fourier transform; Mittag-Leffler kernel; Caputo–Fabrizio fractional differential equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This study aims to use the fractional Fourier transform for analyzing various types of Hyers–Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers–Ulam–Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.
引用
收藏
相关论文
共 50 条
  • [1] A study on fractional differential equations using the fractional Fourier transform
    Hammachukiattikul, Porpattama
    Mohanapriya, Arusamy
    Ganesh, Anumanthappa
    Rajchakit, Grienggrai
    Govindan, Vediyappan
    Gunasekaran, Nallappan
    Lim, Chee Peng
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [2] Analytical solutions of linear fractional partial differential equations using fractional Fourier transform
    Mahor, Teekam Chand
    Mishra, Rajshree
    Jain, Renu
    Journal of Computational and Applied Mathematics, 2021, 385
  • [3] Analytical solutions of linear fractional partial differential equations using fractional Fourier transform
    Mahor, Teekam Chand
    Mishra, Rajshree
    Jain, Renu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 385
  • [4] Fractional Fourier Transform to Stability Analysis of Fractional Differential Equations with Prabhakar Derivatives
    Deepa, S.
    Ganesh, A.
    Ibrahimov, V.
    Santra, S. S.
    Govindan, V.
    Khedher, K. M.
    Noeiaghdam, S.
    AZERBAIJAN JOURNAL OF MATHEMATICS, 2022, 12 (02): : 131 - 153
  • [5] Modified Fourier Transform for Solving Fractional Partial Differential Equations
    Hasanah, Dahliatul
    Sisworo
    Supeno, Imam
    3RD INTERNATIONAL CONFERENCE ON MATHEMATICS AND SCIENCE EDUCATION (ICOMSE) 2019: STRENGTHENING MATHEMATICS AND SCIENCE EDUCATION RESEARCH FOR THE CHALLENGE OF GLOBAL SOCIETY, 2020, 2215
  • [6] FRACTIONAL COMPLEX TRANSFORM FOR FRACTIONAL DIFFERENTIAL EQUATIONS
    Li, Zheng-Biao
    He, Ji-Huan
    MATHEMATICAL AND COMPUTATIONAL APPLICATIONS, 2010, 15 (05) : 970 - 973
  • [7] Solution of fractional integro-differential equations by using fractional differential transform method
    Arikoglu, Aytac
    Ozkol, Ibrahim
    CHAOS SOLITONS & FRACTALS, 2009, 40 (02) : 521 - 529
  • [8] Solution of fractional differential equations by using differential transform method
    Arikoglu, Aytac
    Ozkol, Ibrahim
    CHAOS SOLITONS & FRACTALS, 2007, 34 (05) : 1473 - 1481
  • [9] Fractional differential equations solved by using Mellin transform
    Butera, Salvatore
    Di Paola, Mario
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (07) : 2220 - 2227
  • [10] Solution of Fractional Differential Equations by Using Conformable Fractional Differential Transform Method with Adomian Polynomials
    Teppawar, R. S.
    Ingle, R. N.
    Muneshwar, R. A.
    MATHEMATICS AND COMPUTING, ICMC 2022, 2022, 415 : 349 - 362
12345