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M-fractional derivative under interval uncertainty: Theory, properties and applications

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  • Salahshour, S.
  • Ahmadian, A.
  • Abbasbandy, S.
  • Baleanu, D.

Abstract

In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherit the classical properties from the first order derivative. In this regards, the truncated M-fractional derivative for α-differentiable function was recently introduced that is a generalization of four fractional derivatives presented in the literature and has their important features. In this research, we aim to generalize this novel and effective derivative under interval uncertainty. The concept of interval truncated M-fractional derivative is introduced and some of the distinguished properties of this interesting fractional derivative such as Rolle’s and mean value theorems, are developed for the interval functions. In addition, the existence and uniqueness conditions of the solution for the interval fractional differential equations (IFDEs) based on this new derivative are also investigated. Finally, we present the applicability of this novel interval fractional derivative for IFDEs based on the notion of w-increasing (w-decreasing) by solving a number of test problems.

Suggested Citation

  • Salahshour, S. & Ahmadian, A. & Abbasbandy, S. & Baleanu, D., 2018. "M-fractional derivative under interval uncertainty: Theory, properties and applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 84-93.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:84-93
    DOI: 10.1016/j.chaos.2018.10.002
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    References listed on IDEAS

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    1. Garra, Roberto & Taverna, Giorgio S. & Torres, Delfim F.M., 2017. "Fractional Herglotz variational principles with generalized Caputo derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 94-98.
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    Cited by:

    1. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Muhammad Imran Asjad & Saif Ur Rehman & Ali Ahmadian & Soheil Salahshour & Mehdi Salimi, 2021. "First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    3. Akram, Ghazala & Sadaf, Maasoomah & Zainab, Iqra, 2022. "Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Zhang, Chuang-liang & Huang, Nan-jing & O’Regan, Donal, 2023. "On variational methods for interval-valued functions with some applications," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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