NEW GENERALIZATION INVOLVING CONVEX FUNCTIONS VIA ℠-DISCRETE 𠒜ℬ-FRACTIONAL SUMS AND THEIR APPLICATIONS IN FRACTIONAL DIFFERENCE EQUATIONS

Saima Rashid (), Aasma Khalid (), Yeliz Karaca (), Zakia Hammouch () and Yu-Ming Chu
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Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Aasma Khalid: Department of Mathematics, Government College Women University, Faisalabad, Pakistan
Yeliz Karaca: University of Massachusetts Medical School, Worcester, MA 01655, USA
Zakia Hammouch: Division of Applied mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China6Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-17

Abstract: The purpose of this paper is to explore novel variants for convex functions via discrete 𠒜ℬ-fractional operator in the frame of time scale calculus ℠ℤ with 0 < α < 1 and 0 < ℠≤ 1. Based on a comparison with the integral inequalities, we have provided new discrete fractional inequalities having ℠-discrete generalized Mittag-Leffler function in the kernel which generates several known results and can be utilized as handy tools in the investigation of qualitative and quantitative properties of solutions of certain classes of difference equations. Several new special cases are also apprehended in the setting of time scale ℤ and 𠕋. As the application aspect, we provide an illustrated example to show the effectiveness of our new criteria in fractional ℠-difference type initial value problem.

Keywords: Convex Functions; Discrete Fractional Inequality; â„ -Nabla Fractional Operator; â„ -Discrete Generalized Mittag-Leffler Function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2240134X

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