EXTENSIONS OF FRACTIONAL INTEGRAL INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Hala H. Taha; Yasmeen Razia; Ghulam Farid; Saleem Ullah; Jongsuk Ro

doi:10.11948/20250363

2026 Volume 16 Issue 6

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Hala H. Taha, Yasmeen Razia, Ghulam Farid, Saleem Ullah, Jongsuk Ro. EXTENSIONS OF FRACTIONAL INTEGRAL INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 3232-3243. doi: 10.11948/20250363

Citation:

Hala H. Taha, Yasmeen Razia, Ghulam Farid, Saleem Ullah, Jongsuk Ro. EXTENSIONS OF FRACTIONAL INTEGRAL INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 3232-3243. doi: 10.11948/20250363

EXTENSIONS OF FRACTIONAL INTEGRAL INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
3.
Department of Mathematics, Air University Islamabad, Islamabad 44000, Pakistan
4.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea

Author Bio: Email: hhtaha@pnu.edu.sa(H. H. Taha); Email: sp24-rmt-004@cuilahore.edu.pk(Y. Razia); Email: drghulamfarid@cuilahore.edu.pk(G. Farid); Email: saleemullah314@hotmail.com(S. Ullah)
Corresponding author: Email: jsro@cau.ac.kr(J. Ro)

Abstract

Abstract

The paper introduces new generalizations of well-known inequalities for convex functions using the Katugampola fractional integral, a powerful extension of the Riemann–Liouville fractional integral. Based on basic inequalities, we establish new estimates within the context of Katugampola fractional operators. The results are proven for convex and symmetric convex functions, with proofs that make use of integral representations, kernel properties, and estimations based on convexity. In addition, we have improved estimates for differentiable functions with convex-in-modulus derivatives. These findings offer a unifying and broad framework for fractional integral inequalities, complementing the current literature and paving the way for potential applications in fractional differential equations and functional analysis.
- Fractional integrals /
- Hermite-Hadamard inequality /
- convex functions
MSC: 26A24, 26A33, 26A51, 26B15, 33E12

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References

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