Osama Oqilat

57195353514

Publications - 4

Controlled Fuzzy 2-Metric Spaces: A Soft Computing Framework with Dynamic Applications

Clemente Cesarano Osama Oqilat Hijaz Ahmad Tarapada Bag Abhishikta Das Waleed Mohammed Abdelfattah Dipti Barman Osama Oqilat

Publication Name: International Journal of Analysis and Applications

Publication Date: 2026-01-01

Volume: 24

Issue: Unknown

Page Range: Unknown

Description:

In this article, we introduce the concept of a controlled fuzzy 2-metric space, formulated by incorporating three control functions that flexibly regulate the fuzzy distance relationships among triplets of points. This structure provides a flexible analytical tool for modeling systems influenced by uncertainty, interdependence, and approximate reasoning. We establish several fundamental properties of this structure and derive fixed-point results. To demonstrate its practical relevance, we apply the proposed framework to a dynamic market-equilibrium problem, in which agents’ interactions are governed by fuzzy relations and control-dependent adjustments. The study also discusses implications for soft computing and decision-making systems, highlighting the framework’s potential in modeling adaptive and uncertain environments.

Open Access: Yes

DOI: 10.28924/2291-8639-24-2026-110

Hyers–Ulam stability of a nonlinear fractional hybrid dynamic equations on arbitrary time scales via measures of noncompactness

Osama Oqilat Hijaz Ahmad Bikash Gogoi Waleed Mohammed Abdelfattah Tazuddin Ahmed O. Oqilat Fahmida Nishat Yeasmin

Publication Name: Fixed Point Theory and Algorithms for Sciences and Engineering

Publication Date: 2026-12-01

Volume: 2026

Issue: 1

Page Range: Unknown

Description:

This paper investigates different forms of Hyers–Ulam stability for solutions of a nonlinear fractional hybrid dynamic equation defined on arbitrary time scales. By employing the measure of noncompactness together with a newly developed generalized version of Darbo’s fixed-point theorem, the existence of solutions is established. The uniqueness of solutions is further guaranteed via the Banach fixed-point theorem. In addition, illustrative numerical examples are presented to demonstrate the applicability and effectiveness of the theoretical results.

Open Access: Yes

DOI: 10.1186/s13663-026-00839-3

Analysis of Elliptic Inverse Heat Conduction Problems Using a Pascal Polynomial Numerical Approach

Osama Oqilat Muhammad Nawaz Khan Hijaz Ahmad Imtiaz Ahmad O. Oqilat

Publication Name: Journal of Applied and Computational Mechanics

Publication Date: 2026-06-01

Volume: 12

Issue: 3

Page Range: 1201-1216

Description:

This study presents a Pascal polynomial-based numerical framework for solving inverse heat conduction problems governed by the steady-state Poisson equation. The proposed methodology employs the Pascal Polynomial Collocation Method (PPCM) and its regularized variant (PPCM-T) to reconstruct unknown boundary conditions and source terms in two-dimensional bounded domains. Two complementary strategies are adopted: one directly approximates both the temperature field and the unknown source term using Pascal polynomials, while the other reformulates the inverse problem as a direct fourth-order system by assuming that the unknown source satisfies Laplace's equation. Several benchmark examples defined over rectangular and annular geometries are investigated to assess the method's accuracy and stability. The results demonstrate that both PPCM and PPCM-T achieve excellent agreement with analytical or reference solutions under noise-free data, with systematic error reduction as the number of collocation nodes increases. Under noisy boundary data, PPCM-T exhibits superior robustness due to its built-in regularization, maintaining acceptable accuracy and numerical stability. Overall, the Pascal polynomial-based framework provides a flexible, mesh-free, and computationally efficient approach for addressing inverse elliptic and heat conduction problems, offering strong potential for broader applications in computational mechanics and thermal analysis.

Open Access: Yes

DOI: 10.22055/jacm.2026.48835.5535

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