Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 14Citation - Scopus: 18Strong Interaction of Jafari Decomposition Method With Nonlinear Fractional-Order Partial Differential Equations Arising in Plasma Via the Singular and Nonsingular Kernels(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Jarad, Fahd; Rashid, SaimaThis research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.Article Citation - WoS: 4Citation - Scopus: 4A Novel Formulation of the Fuzzy Hybrid Transform for Dealing Nonlinear Partial Differential Equations Via Fuzzy Fractional Derivative Involving General Order(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; Alqurashi, M. S.The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order 0 < alpha < r) considering all relevant permutations of entities involving t(1) equal to 1 and t(2) (the others) equal to 2 via fuzz Under gH-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order alpha is an element of (r - 1, r). Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adorn ian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via gH-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.Article Citation - WoS: 17Citation - Scopus: 17The Analytical Analysis of Nonlinear Fractional-Order Dynamical Models(Amer inst Mathematical Sciences-aims, 2021) Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Xu, JiabinThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.