Fractional differential equations of variable order: existence results, numerical method and asymptotic stability conditions

  • Guo-Cheng Wu, Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PR China,
  • Chuan-Yun Gu, School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, PR China,
  • Lan-Lan Huang, School of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan Province, PR China,
  • Dumitru Baleanu, Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey; Institute of Space Sciences, Magurele–Bucharest, Romania ,


New variable-order fractional differential equations are proposed and numerical solutions are given in this paper. Firstly, a new way is introduced to define variable--order functions. The initial conditions are varied on different intervals and the fractional differential equations hold short memory effects or short-term interactions. Existence results are provided by Banach fixed point theorem successively over different intervals. Finally, predictor corrector method is improved and numerical examples are illustrated accordingly.

Vol. 23 (2022), No. 1, pp. 485-493
DOI: 10.18514/MMN.2022.2730

Download: MMN-2730