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http://dx.doi.org/10.7858/eamj.2018.018

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)
Publication Information
East Asian mathematical journal / v.34, no.3, 2018 , pp. 249-263 More about this Journal
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.
Keywords
fractional integral; fractional derivative; k-fractional integral; k-fractional derivative; Hadamard k-fractional derivative; fractional integral inequalities; Gronwall type inequalities;
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