Ali Asghar

59969923100

Publications - 4

Some New Notions of Mathematical Integral Inequalities: Theory and Applications

Maggie Aphane Muhammad Tariq Hijaz Ahmad Ali Asghar Waqar Afzal Rakib Efendiev

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 play a fundamental role in both pure and applied sciences. In this work, we first explore the notion of n-fractional polynomial s-like m-convexity involving Raina’s mapping and also its algebraic properties. We then introduce a novel Hermite–Hadamard (H-H), midpoint H-H, trapezoid H-H type inequalities based on this generalized concept and the k-fractional operator. Several related corollaries and examples are examined, particularly in connection with the Mittag–Leffler function. The practical utility of the proposed inequalities is demonstrated through applications to viscoelastic materials with fractional damping, supported by computational algorithms, and a numerical example involving fractional diffusion in fractured media. The results provide meaningful refinements and novel insights that extend and enrich existing research in the field.

Open Access: Yes

DOI: 10.28924/2291-8639-24-2026-175

Some New Approaches of Hermite-Hadamard Type Inequalities Pertaining to Generalized Convexity on Coordinates Using Hypergeometric Function

Osama Oqilat Muhammad Tariq Hijaz Ahmad M. Nadeem Ali Asghar O. Oqilat Rakib Efendiev

Publication Name: Azerbaijan Journal of Mathematics

Publication Date: 2026-01-01

Volume: 16

Issue: 1

Page Range: 220-257

Description:

In this study, we develop a class of generalized fractional inequalities by employing (m, n)-polynomial (p1, p2)-convex functions defined on the coordinates. A novel integral identity for functions of two variables is established, serving as a key tool in our analysis. Furthermore, we derive new sort of Hermite-Hadamard-type inequality through generalized fractional operators. In addition, we present some new refinements of Hermite-Hadamard type inequality via (m, n)-polynomial (p1, p2)-convex functions with the help of hypergeometric functions. This framework provides a unified approach that encompasses several existing concepts, including (m, n)-polynomial harmonic convexity, (m, n)-polynomial convexity, classical harmonic convexity, and classical convexity, all obtained as specific instances of our results. Consequently, the findings presented here not only extend previously known inequalities but also recover a number of recent contributions in the literature as particular cases.

Open Access: Yes

DOI: 10.59849/2218-6816.2026.1.220

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

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