Browsing by Author "Kanwal, Bushra"

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Citation - WoS: 4
Citation - Scopus: 4
A 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) Alqurashi, M. S.; Jarad, Fahd; Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; 234808; Matematik
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.
Citation - WoS: 7
Citation - Scopus: 7
A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model
(Elsevier, 2022) Rashid, Saima; Jarad, Fahd; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; 234808; Matematik
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, R-0, 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.
Citation - WoS: 3
Citation - Scopus: 3
Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; 234808; Matematik
Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming gH-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor pi is an element of [0, 1] which encompasses the varying fractional values. Finally, the EADM is predicted to be e ffective and precise in generating the analytical results for dynamical fuzzy fractional partial di fferential equations that emerge in scientific disciplines.