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001-es BibID:	BIBFORM114499
035-os BibID:	(cikkazonosító)673 (WoS)001074676300001 (Scopus)85172107949
Első szerző:	Ashraf, Rashid
Cím:	A New Hybrid Optimal Auxiliary Function Method for Approximate Solutions of Non-Linear Fractional Partial Differential Equations / Rashid Ashraf , Rashid Nawaz, Osama Alabdali, Nicholas Fewster-Young, Ali Hasan Ali, Firas Ghanim, Alina Alb Lupas
Dátum:	2023
ISSN:	2504-3110
Megjegyzések:	This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann-Liouville`s fractional integral and the Caputo derivative. This approach eliminates the need for assumptions about parameter magnitudes, offering a significant advantage. We validate our approach using the time-fractional Cahn-Hilliard, fractional Burgers-Poisson, and Benjamin-Bona-Mahony-Burger equations. Comparative testing shows that our method outperforms new iterative, homotopy perturbation, homotopy analysis, and residual power series methods. These examples highlight our method`s effectiveness in obtaining precise solutions for non-linear fractional differential equations, showcasing its superiority in accuracy and consistency. We underscore its potential for revealing elusive exact solutions by demonstrating success across various examples. Our methodology advances fractional differential equation research and equips practitioners with a tool for solving non-linear equations. A key feature is its ability to avoid parameter assumptions, enhancing its applicability to a broader range of problems and expanding the scope of problems addressable using fractional calculus techniques.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk
Megjelenés:	Fractal and Fractional. - 7 : 9 (2023), p. 1-18. -
További szerzők:	Nawaz, Rashid Alabdali, Osama Fewster-Young, Nicholas Ali, Ali Hasan (1989-) (matematikus) Ghanim, Firas Alb Lupas, Alina
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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001-es BibID:	BIBFORM114720
035-os BibID:	(cikkazonosító)881 (WoS)001072546200001 (Scopus)85172116611
Első szerző:	Nawaz, Rashid
Cím:	A New Extension of Optimal Auxiliary Function Method to Fractional Non-Linear Coupled ITO System and Time Fractional Non-Linear KDV System / Rashid Nawaz, Aaqib Iqbal, Hina Bakhtiar, Wissal Audah Alhilfi, Nicholas Fewster-Young, Ali Hasan Ali, Ana Danca Poțclean
Dátum:	2023
ISSN:	2075-1680
Megjegyzések:	In this article, we investigate the utilization of Riemann-Liouville`s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze fractional non-linear coupled ITO systems and non-linear KDV systems, which feature equations of a fractional order in time. We compare the results obtained for the ITO system with those derived from the Homotopy Perturbation Method (HPM) and the New Iterative Method (NIM), and for the KDV system with the Laplace Adomian Decomposition Method (LADM). OAFM demonstrates remarkable convergence with a single iteration, rendering it highly effective. In contrast to other existing analytical approaches, OAFM emerges as a dependable and efficient methodology, delivering high-precision solutions for intricate problems while saving both computational resources and time. Our results indicate superior accuracy with OAFM in comparison to HPM, NIM, and LADM. Additionally, we enhance the accuracy of OAFM through the introduction of supplementary auxiliary functions.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk optimal auxiliary function method (OAFM) riemann-liouville integral modified riemann-liouville derivatives time fractional coupled ITO system non-linear KDV system of time fractional order Caputo fractional derivative
Megjelenés:	Axioms. - 12 : 9 (2023), p. 1-17. -
További szerzők:	Iqbal, Aaqib Bakhtiar, Hina Alhilfi, Wissal Audah Fewster-Young, Nicholas Ali, Ali Hasan (1989-) (matematikus) Potcelan, Ana Danca
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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001-es BibID:	BIBFORM119575
Első szerző:	Rehman, Siddiq Ur
Cím:	A comparative analysis of Noyes-Field model for the non-linear Belousov-Zhabotinsky reaction using two reliable techniques / Siddiq Ur Rehman, Rashid Nawaz, Faisal Zia, Nicholas Fewster-Young, Ali Hasan Ali
Dátum:	2024
ISSN:	1110-0168 2090-2670
Megjegyzések:	Within the domain of nonlinear dynamics, the Belousov-Zhabotinsky reaction system has consistently captivated researchers, sustaining its position as a vibrant and dynamic area of exploration. As an enduring subject of study, the Belousov-Zhabotinsky system provides continuous opportunities to unravel the foundational tenets of nonlinear dynamics within intricate systems. In our quest to deepen comprehension of this complex system, we introduce an innovative methodology for addressing the time fractional Belousov-Zhabotinsky system. This novel approach leverages both the Natural Transform Iterative Method (NTIM) and the Optimal Homotopy Asymptotic Method (OHAM), aiming to contribute novel insights and methodologies to the ongoing discourse surrounding this intriguing and influential area of research. We obtained a series solution to test the accuracy of the suggested approach. The proposed technique has the advantage of requiring few calculations while producing high-precision results. To help you better understand, 2D and 3D graphical representations are provided to demonstrate the model`s behavior and how changing the fractional order derivative in Caputo`s sense and time affects the solutions.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Belousov-Zhabotinsky system Natural transform iterative method Caputo operator Optimal homotopy asymptotic method
Megjelenés:	Alexandria Engineering Journal. - 93 (2024), p. 259-279. -
További szerzők:	Nawaz, Rashid Zia, Faisal Fewster-Young, Nicholas Ali, Ali Hasan (1989-) (matematikus)
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