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The Youngnam Mathematical Society (영남수학회)
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CERTAIN GRONWALL TYPE INEQUALITIES ASSOCIATED WITH RIEMANN-LIOUVILLE k- AND HADAMARD k-FRACTIONAL DERIVATIVES AND THEIR APPLICATIONS

  • Nisar, Kottakkaran Sooppy (Department of Mathematics, College of Arts and Science-Wadi Aldawaser, Prince Sattam bin Abdulaziz University) ;
  • Rahman, Gauhar (Department of Mathematics, International Islamic University) ;
  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Mubeen, Shahid (Department of Mathematics, University of Sargodha) ;
  • Arshad, Muhammad (Department of Mathematics, International Islamic University)
  • Received : 2018.01.31
  • Accepted : 2018.02.19
  • Published : 2018.05.31
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Abstract

We aim to establish certain Gronwall type inequalities associated with Riemann-Liouville k- and Hadamard k-fractional derivatives. The results presented here are sure to be new and potentially useful, in particular, in analyzing dependence solutions of certain k-fractional differential equations of arbitrary real order with initial conditions. Some interesting special cases of our main results are also considered.

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References

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