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AIMS Mathematics

2022, Volume 7, Issue 5: 7489-7506. doi: 10.3934/math.2022420
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Research article

Nonlinear higher order fractional terminal value problems

  • 1.
    Cankaya University, Department of Mathematics, 06530 Balgat, Ankara, Turkey
  • 2.
    Institute of Space Sciences, Magurele-Bucharest, Romania
  • 3.
    Department of Medical Research, China Medical University Hospital, China Medical, University, Taichung, Taiwan
  • 4.
    Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China
  • Received: 07 December 2021 Revised: 16 January 2022 Accepted: 24 January 2022 Published: 14 February 2022

  • MSC : 34A08, 45G05

  • Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.

    Citation: Dumitru Baleanu, Babak Shiri. Nonlinear higher order fractional terminal value problems[J]. AIMS Mathematics, 2022, 7(5): 7489-7506. doi: 10.3934/math.2022420

    Related Papers:

  • Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.


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