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ARTICLE

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag–Leffler Function in the Kernel

Saima Rashid¹, Zakia Hammouch², Rehana Ashraf³, Yu-Ming Chu^4,*
1 Department of Mathematics, Government College University, Faisalabad, Pakistan
2 Division of Applied mathematics, Thu Dau Mot University, Thu Dau Mot City, Vietnam
3 Department of Mathematics, Lahore College Women University, Jhangh Campus, Lahore, Pakistan
4 Department of Mathematics, Huzhou University, Huzhou, China
* Corresponding Author: Yu-Ming Chu. Email:
(This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 126(1), 359-378. https://doi.org/10.32604/cmes.2021.011782

Received 29 May 2020; Accepted 08 September 2020; Issue published 22 December 2020

Abstract

In the present case, we propose the novel generalized fractional integral operator describing Mittag–Leffler function in their kernel with respect to another function Ф. The proposed technique is to use graceful amalgamations of the Riemann–Liouville (RL) fractional integral operator and several other fractional operators. Meanwhile, several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n (n ∈ N) for the proposed fractional operator. In order to confirm and demonstrate the proficiency of the characterized strategy, we analyze existing fractional integral operators in terms of classical fractional order. Meanwhile, some special cases are apprehended and the new outcomes are also illustrated. The obtained consequences illuminate that future research is easy to implement, profoundly efficient, viable, and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

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Keywords

Integral inequality; generalized fractional integral with respect to another function; increasing and decreasing functions; Mittag–Leffler function

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Citations