Browsing by Author "Elagan, S.K."

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Citation Count: Alqurashi, M.S.;...et.al. (2022). "A novel formulation of the fuzzy hybrid transform for dealing nonlinear partial differential equations via fuzzy fractional derivative involving general order", AIMS Mathematics, Vol.7, No.8, pp.14946-14974.
A novel formulation of the fuzzy hybrid transform for dealing nonlinear partial differential equations via fuzzy fractional derivative involving general order
(2022) Alqurashi, M.S.; Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S.K.; 234808
The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order 0 < α < r) considering all relevant permutations of entities involving t1 equal to 1 and t2 (the others) equal to 2 via fuzzifications. Under gH-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order α ∈ (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 Adomian 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.
Citation Count: Rashid, Saima;...et.al. (2022). "A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model", Results in Physics, Vol.38.
A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model
(2022) Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S.K.; 234808
In this paper, we provide a generic mathematical framework for scabies transmission mechanisms. The infections involving susceptible, highly contagious people and juvenile scabiei mites are characterized by a framework of ordinary differential equations (DEs). The objective of this study is to examine the evolution of scabies disease employing a revolutionary configuration termed a fractal–fractional (FF) Atangana–Baleanu (AB) operator. Generic dynamical estimates are used to simulate the underlying pace of growth of vulnerable people, clinical outcomes, and also the eradication and propagation rates of contaminated people and immature mites. We study and comprehend our system, focusing on a variety of restrictions on its basic functionalities. The model's outcomes are assessed for positivity and boundedness. The formula includes a fundamental reproducing factor, R0, that ensures the presence and stability of all relevant states. Furthermore, the FF-AB operator is employed in the scabies model, and its mathematical formulation is presented using a novel process. We analyze the FF framework to construct various fractal and fractional levels and conclude that the FF theory predicts the affected occurrences of scabies illness adequately. The relevance and usefulness of the recently described operator has been demonstrated through simulations of various patterns of fractal and fractional data.