Evren Hincal

26635282900

Publications - 3

New Fractional Approach of Hermite-Hadamard-Type Inequalities with Applications to Information Divergence and Entropy Bounds

Evren Hincal Muhammad Tariq Hijaz Ahmad Tonguc Cagin Ilyas Khan Waleed Mohammed Abdelfattah Ali Asghar Waqar Afzal Saima Bhatti

Publication Name: International Journal of Analysis and Applications

Publication Date: 2026-01-01

Volume: 24

Issue: Unknown

Page Range: Unknown

Description:

Fractional integral operators play a vital role in establishing generalized forms of mathematical inequalities. These operators provide effective tools for modeling various scientific and engineering processes such as fracture mechanics, elasticity, heat transfer, viscoelastic deformation, and the behavior of continuous populations. In this study, we investigate a new class of Hermite–Hadamard type inequalities and verify their numerical validity. By employing a novel equality together with Hölder’s inequality, we derive several extensions of Hermite–Hadamard type inequalities through generalized convexity involving Raina’s function within the framework of fractional integral operators. Moreover, we present applications related to information divergence and entropy bounds. The results obtained here constitute significant advancements and generalizations of existing findings in the literature.

Open Access: Yes

DOI: 10.28924/2291-8639-24-2026-204

Boundedness Properties of Multidimensional Fractional Hadamard-Type Operators on Campanato Spaces

Evren Hincal Khurram Shabbir Mutum Zico Meetei Haitham Qawaqneh Muhammad Tariq Hijaz Ahmad Waqar Afzal Mohammed Abbas Ei-Naggar

Publication Name: International Journal of Analysis and Applications

Publication Date: 2026-01-01

Volume: 24

Issue: Unknown

Page Range: Unknown

Description:

The present work aims to extend the one-dimensional Hadamard fractional operator to a general multidimensional setting and study how this newly built operator acts between two Campanato spaces, Kp,µ (D) and Kq,ν (D). Alongside the boundedness statement itself, we pin down an explicit rate at which the operator norm grows with the diameter of D. Two features distinguish this study from prior boundedness results for fractional-type operators. First, the Campanato scale is strictly finer than the Morrey scale on which such questions are usually posed. Second, the Hadamard operator sits inside the Katugampola family as the degenerate case ρ → 0+, carrying a logarithmic kernel (log v σ)s−1 in place of the power kernels that dominate the classical theory – and it is exactly this logarithmic structure that drives the sharper estimates obtained below.

Open Access: Yes

DOI: 10.28924/2291-8639-24-2026-200

New Variant of Hermite-Hadamard-Type Inequality with Applications to Matrix and Bivariate Analysis

Evren Hincal Muhammad Tariq Hijaz Ahmad Ilyas Khan Waleed Mohammed Abdelfattah Ali Asghar Waqar Afzal Saima Bhatti Mustafa Bayram

Publication Name: International Journal of Analysis and Applications

Publication Date: 2026-01-01

Volume: 24

Issue: Unknown

Page Range: Unknown

Description:

Convex analysis and mathematical inequalities are now essential to the development of numerous pure and applied scientific domains. In this article, first we introduce the concept of n-fractional polynomial s-like m-preinvex function. In addition, we introduce, the new variant of Hermite-Hadamard type inequality via newly introduced concept pertaining to the k-fractional operator. Furthermore, we demonstrate the applications to matrix and bivariat analysis via newly introduce Hermite-Hadamard type inequality. The study’s conclusions present unique perspectives and contributions to the field, offering fresh and noteworthy improvements over previous research.

Open Access: Yes

DOI: 10.28924/2291-8639-24-2026-220