ACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE

Maysaa Al-Qurashi (), Saima Rashid (), Yeliz Karaca (), Zakia Hammouch, Dumitru Baleanu () and Yu-Ming Chu
Additional contact information
Maysaa Al-Qurashi: Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, 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, Vietnam5Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan6Ecole Normale Supérieure, Moulay Ismail University of Meknes, 5000, Morocco
Dumitru Baleanu: Department of Mathematics, Çankaya University, Ankara, Turkey
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-18

Abstract: A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Čebyšev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Čebyšev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.

Keywords: Integral Inequality; Generalized Proportional Fractional Operator in the Hilfer Sense; Čebyšev Inequality; Generalized Riemann–Liouville Fractional Integral (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400272

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