AIMS Mathematics, 2019, 4(3): 343-358. doi: 10.3934/math.2019.3.343

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Generalized k-fractional conformable integrals and related inequalities

1 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China
2 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
3 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China
4 Department of Mathematics, Government College University Faisalabad, Pakistan
5 Department of Mathematics, University of Sargodha, Sargodha, Pakistan
6 Department of Mathematics, Government College University Faisalabad, Pakistan, Siddra Habib, Shahid Mubeen, Muhammad Nawaz Naeem

In the paper, the authors introduce the generalized k-fractional conformable integrals, which are the k-analogues of the recently introduced fractional conformable integrals and can be reduced to other fractional integrals under specific values of the parameters involved. Hereafter, the authors prove the existence of k-fractional conformable integrals. Finally, the authors generalize some integral inequalities to ones for generalized k-fractional conformable integrals.
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