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1.

001-es BibID:BIBFORM129955
035-os BibID:(Scopus)105004893254
Első szerző:Altaie, Huda Omran
Cím:A hybrid analytical method for fractional order Klein-Gordon and Burgers equations / Huda Omran Altaie, Adel Rashed A. Ali, Ghaith Fadhil Abbas, Ali Hasan Ali
Dátum:2025
ISSN:2666-8181
Megjegyzések:In this study, fractional-order partial differential equations (FPDEs), specifically the Klein-Gordon equation (KGE) and the Burgers equation, are analytically solved using a modified and combined version of the Elzaki Decomposition Technique (ETADM). To assess the efficacy and robustness of the proposed approach, several examples are provided to obtain analytical and numerical results related to the KGE and the Burgers equation. Furthermore, the proposed techniques yield convergent series solutions with well-defined components, without the need for perturbation or linearization. Additionally, we compare several methods for solving differential equations arising in physics and engineering, including ETADM, the Variational Iteration Method (VIM), and the Adomian Decomposition Method (ADM). For comparison and validation, three examples are presented, along with the results obtained using both ETADM and VIM.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Megjelenés:Partial Differential Equations in Applied Mathematics. - 14 (2025), p. 1-7. -
További szerzők:Ali, Adel Rashed A. Abbas, Ghaith Fadhil Ali, Ali Hasan (1989-) (matematikus)
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2.

001-es BibID:BIBFORM126869
Első szerző:Bilal, Muhammad
Cím:Comparative rheological features of radiated Darcy-Forchheimer flow of micropolar and second grade fluid with cross diffusion and Arrhenius activation energy / S. Bilal, Muhammad Yasir, Ali Hasan Ali
Dátum:2025
ISSN:2666-8181
Megjegyzések:The main intension of this study is to scrutinize the transient flow characteristics of two different non-Newtonian models of micropolar fluid and second grade fluid subject to a stretchable Riga plate. This novel study communicates with the rotational motion of microelements by taking into account the strong and weak concentrations and incompressible Darcy Forchheimer flow features of second grade fluid. In the context of Dufour and Soret effects, the cross-diffusion process is analyzed in the mechanisms of mass and heat transport. Moreover, Buongiorno model is taken into account to deliberate the random movement of particles and thermophoretic effects in both considered fluids. The consequences of convective constraint, Arrhenius activation energy, and joule heating are also incorporated. The framework of ordinary dimensionless equations is accomplished by deploying convenient variables and numerically processed via reliable bpv4c technique in MATLAB. The rheology of both considered fluids is compared through graphics regarding different concentration level and pertinent parameters. Micropolar fluid has higher intensity of its dynamical behavior as compared to second grade fluid. Moreover, the improved activation energy parameter lowers the nature of both considered fluids.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Megjelenés:Partial Differential Equations in Applied Mathematics. - 13 (2025), p. 1-9. -
További szerzők:Yasir, Muhammad Ali, Ali Hasan (1989-) (matematikus)
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3.

001-es BibID:BIBFORM120957
035-os BibID:(Scopus)85192183478
Első szerző:Ismael, Mimoon
Cím:Modified optimal auxiliary functions method for approximate-analytical solutions in fractional order nonlinear Foam Drainage equations / Mimoon Ismael, Saba Hat, Osama Alabdali, Showkat Ahmad Lone, Ali Hasan Ali
Dátum:2024
ISSN:2666-8181
Megjegyzések:The study aims to obtain new approximate analytical solutions for the fractional order nonlinear Foam Drainage equation through a novel modification of the well-known Optimal Auxiliary Functions Method (OAFM). This method systematically constructs auxiliary functions, and by optimizing their parameters, it provides approximate solutions closely mirroring the original behavior of the problem. Numerical simulations, presented in tabular form, demonstrate the effectiveness of the proposed approach. Graphical representations of the solutions are utilized to further validate the applicability and accuracy of the suggested technique. Additionally, the results affirm that the modified OAFM stands out as one of the most effective tools for addressing nonlinear problems in the field of science and technology, thereby contributing valuable addition to the field.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Optimal auxiliary functions method
Foam Drainage equation
Caputo operator
Approximation
Fractional equations
Megjelenés:Partial Differential Equations in Applied Mathematics. - 10 (2024), p. 1-6. -
További szerzők:Hat, Saba Alabdali, Osama Lone, Showkat Ahmad Ali, Ali Hasan (1989-) (matematikus)
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4.

001-es BibID:BIBFORM125033
035-os BibID:(Scopus)85206251696
Első szerző:Khalil, Muayyad Mahmood
Cím:New modifications of natural transform iterative method and q-homotopy analysis method applied to fractional order KDV-Burger and Sawada-Kotera equations / Muayyad Mahmood Khalil, Siddiq Ur Rehman, Ali Hasan Ali, Rashid Nawaz, Belal Batiha
Dátum:2024
ISSN:2666-8181
Megjegyzések:This manuscript presents enhanced versions of two methods: the natural transform iterative method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness concepts from Fractional Calculus, particularly leveraging the Caputo fractional derivative operator, to successfully manage the complexities of fractional-order systems. To validate their accuracy and efficiency, we applied the proposed techniques to FPDEs like the fractional-order KDV-Burger and fifth-order Sawada-Kotera equations. Our outcomes, which closely resemble the exact solutions, demonstrate how useful NTIM and q-HAM are for solving difficult FPDEs and improving the study of fractional calculus.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
fractional calculus
fifth-order Sawada-Kotera equation
fractional nonlinear KDV-burgers
q-homotopy analysis method
caputo operator
natural transform iterative method
Megjelenés:Partial Differential Equations in Applied Mathematics. - 12 (2024), p. 1-9. -
További szerzők:Rehman, Siddiq Ur Ali, Ali Hasan (1989-) (matematikus) Nawaz, Rashid Batiha, Belal
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5.

001-es BibID:BIBFORM115350
035-os BibID:(Scopus)85174056521
Első szerző:Khan, Ibrar
Cím:Comparative analysis of the fractional order Cahn-Allen equation / Ibrar Khan, Rashid Nawaz, Ali Hasan Ali, Ali Akgul, Showkat Ahmad Lone
Dátum:2023
ISSN:2666-8181
Megjegyzések:This current work presents a comparative study of the fractional-order Cahn-Allen (CA) equation, where the non-integer derivative is taken in the Caputo sense.The Cahn-Allen equation is an equation that assists in the comprehension of phase transitions and pattern formation in physical systems. This equation describes how different phases of matter, such as solids and liquids, change and interact throughout time. We employ two analytical methods: the Laplace Residual Power Series Method (LRPSM) and the New Iterative Method (NIM), to solve the proposed model. The LRPSM is a combination of the Laplace Transform and the Residual Power Series Method, while the New Iterative Method is a modified form of the Adomian Decomposition Method that does not require any type of polynomial or digitization. For the purpose of accuracy and reliability, we compare our findings with other methods and the exact solution used in the literature. Additionally, 2D and 3D plots are generated for various fractional order values denoted as p. These plots illustrate that as the fractional order p approaches 1, the graph of the approximate solution gradually coincides with the graph of the exact solution.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Laplace residual power series
Fractional-order Cahn-Allen equation
Laplace transform
Caputo operator
Megjelenés:Partial Differential Equations in Applied Mathematics. - 8 (2023), p. 1-8. -
További szerzők:Nawaz, Rashid Ali, Ali Hasan (1989-) (matematikus) Akgul, Ali Lone, Showkat Ahmad
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6.

001-es BibID:BIBFORM123266
035-os BibID:(Scopus)85199541087
Első szerző:Redhwan, Saleh S.
Cím:New Grüss`s inequalities estimates considering the fí-fractional integrals / Saleh S. Redhwan, Tariq A. Aljaaidi, Ali Hasan Ali, Maryam Ahmed Alyami, Mona Alsulami, Najla Alghamdi
Dátum:2024
ISSN:2666-8181
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
grüss inequalities
fractional inequalities
fí-proportional fractional operators
Megjelenés:Partial Differential Equations in Applied Mathematics. - 11 (2024), p.1-8. -
További szerzők:Aljaaidi, Tariq A. Ali, Ali Hasan (1989-) (matematikus) Alyami, Maryam Ahmed Alsulami, Mona Alghamdi, Najla
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