GENERALIZED k-FRACTIONAL CONFORMABLE INTEGRALS AND RELATED INEQUALITIES

Feng Qi (1, 2, 3) , Siddra Habib (4) , Shahid Mubeen (5) , Muhammad Nawaz Naeem (4)

1 Henan Polytechnic University
2 Tianjin Polytechnic University
3 UESTC - University of Electronic Science and Technology of China [Chengdu]
4 Government College University Faisalabad
5 University of Sargodha

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.

Mots clés: left $k$-fractional conformable integral; right $k$-fractional conformable integral; fractional integral inequality; left k-fractional conformable integral; right k-fractional conformable integral

Domaines: Analyse classique [math.CA]

Feng Qi, Siddra Habib, Shahid Mubeen, Muhammad Nawaz Naeem. GENERALIZED k-FRACTIONAL CONFORMABLE INTEGRALS AND RELATED INEQUALITIES. AIMS Mathematics, 2019, 4 (3), pp.343--358. ⟨10.3934/math.2019.3.343⟩. ⟨hal-01788916v2⟩