OPIAL-TYPE INEQUALITIES IN THE FRAMEWORK OF CONFORMABLE FRACTIONAL CALCULUS

Nadiah Zafer Al-Shehri; Samir H. Saker; Gihad M. Ashry; Mohammed Zakarya; Haytham M. Rezk; Mohammed R. Kenawy

doi:10.11948/20250253

2026 Volume 16 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(5): 2314-2332

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Nadiah Zafer Al-Shehri, Samir H. Saker, Gihad M. Ashry, Mohammed Zakarya, Haytham M. Rezk, Mohammed R. Kenawy. OPIAL-TYPE INEQUALITIES IN THE FRAMEWORK OF CONFORMABLE FRACTIONAL CALCULUS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2314-2332. doi: 10.11948/20250253

Citation:

Nadiah Zafer Al-Shehri, Samir H. Saker, Gihad M. Ashry, Mohammed Zakarya, Haytham M. Rezk, Mohammed R. Kenawy. OPIAL-TYPE INEQUALITIES IN THE FRAMEWORK OF CONFORMABLE FRACTIONAL CALCULUS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2314-2332. doi: 10.11948/20250253

OPIAL-TYPE INEQUALITIES IN THE FRAMEWORK OF CONFORMABLE FRACTIONAL CALCULUS

1.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura 7723730, Egypt
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
4.
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
5.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
6.
Computer Engineering Department, Engineering and Information Technology College, Buraydah Private Colleges, Buraydah 51418, Saudi Arabia

Author Bio: Email: nadia@kku.edu.sa(N. Z. Al-Shehri); Email: shsaker@mans.edu.eg(S. H. Saker); Email: gma07@fayoum.edu.eg(G. M. Ashry); Email: mzibrahim@kku.edu.sa(M. Zakarya); Email: mrz00@fayoum.edu.eg(M. R. Kenawy)
Corresponding author: Email: haythamrezk@azhar.edu.eg(H. M. Rezk)
Fund Project: The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Project under grant number RGP 2/248/46

Abstract

Abstract

This article investigates fractional Opial-type inequalities within the framework of conformable calculus. The results are established using conformable fractional analogues of Hölder's inequality, the integration by parts formula, and the chain rule. Several classical integral Opial-type inequalities are derived as special cases of the main results, demonstrating the generality and applicability of the proposed approach. Notably, the paper highlights a structural symmetry between the new inequalities and those previously established in the literature.
- Generalized inequalities /
- integral inequalities /
- Opial-type inequalities /
- conformable fractional calculus /
- chain rule
MSC: 26D10, 26D15, 34N05, 47B38, 39A12

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