Atangana–Baleanu Derivative with Fractional Order Applied to the Gas Dynamics Equations

  • Sunil KumarEmail author
  • Amit Kumar
  • J. J. Nieto
  • B. Sharma
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 194)


We apply the new Atangana–Baleanu derivative in Caputo sense to study gas dynamics equations of arbitrary order using modified homotopy analysis transform method (MHATM). Atangana and Baleanu suggested an interesting fractional operator in 2016 which is based on the exponential kernel. An alternative framework of MHATM with Atangana–Baleanu derivative is presented and the modified Gas dynamics equations are solved numerically and analytically using aforesaid the method. Illustrative examples are included to demonstrate the validity and applicability of the presented technique with new Atangana–Baleanu derivative.


Fractional calculus Atangana–Baleanu fractional derivative Gas dynamics equations 



The first author Sunil Kumar would like to acknowledge the financial support received from the National Board for Higher Mathematics. Department of Atomic Energy, Government of India (Approval No. 2/48(20)/2016/NBHM(R.P.)/R and D II/1014).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sunil Kumar
    • 1
    Email author
  • Amit Kumar
    • 2
  • J. J. Nieto
    • 3
  • B. Sharma
    • 1
  1. 1.Department of MathematicsNational Institute of TechnologyJamshedpurIndia
  2. 2.Department of MathematicsBalarampur College PuruliaBalarampur, PuruliaIndia
  3. 3.Department of Statistics, Mathematical Analysis and OptimizationUniversity of Santiago de CompostelaSantiago de CompostelaSpain

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