Generalized <em>k</em>-fractional conformable integrals and related inequalities

Feng Qi; Siddra Habib; Shahid Mubeen; Muhammad Nawaz Naeem; Feng Qi; Siddra Habib; Shahid Mubeen; Muhammad Nawaz Naeem

doi:10.3934/math.2019.3.343

AIMS Mathematics

2019, Volume 4, Issue 3: 343-358. doi: 10.3934/math.2019.3.343

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Research article

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

Received: 21 December 2018 Accepted: 25 February 2019 Published: 15 April 2019
MSC : Primary 26A33; Secondary 26D10, 35A23, 47A63

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.
- left k-fractional conformable integral,
- right k-fractional conformable integral,
- fractional integral inequality
Citation: Feng Qi, Siddra Habib, Shahid Mubeen, Muhammad Nawaz Naeem. Generalized k-fractional conformable integrals and related inequalities[J]. AIMS Mathematics, 2019, 4(3): 343-358. doi: 10.3934/math.2019.3.343

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Abstract

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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