WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Rashid, SaimaSubject: search.filters.subject.Atangana-Baleanu Fractional Derivative

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 10
    Citation - Scopus: 11
    Novel Numerical Investigation of the Fractional Oncolytic Effectiveness Model With M1 Virus Via Generalized Fractional Derivative With Optimal Criterion
    (Elsevier, 2022) Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y. S.; Rashid, Saima
    Oncolytic virotherapy is an efficacious chemotherapeutic agent that addresses and eliminates cancerous tissues by employing recombinant infections. M1 is a spontaneously produced oncolytic alphavirus with exceptional specificity and powerful activity in individual malignancies. The objective of this paper is to develop and assess a novel fractional differential equation (FDEs)-based mathematical formalism that captures the mechanisms of oncogenic M1 immunotherapy. The aforesaid framework is demonstrated with the aid of persistence, originality, non-negativity, and stability of systems. Additionally, we also examine all conceivable steady states and the requirements that must exist for them to occur. We also investigate the global stability of these equilibria and the characteristics that induce them to be unstable. Furthermore, the Atangana- Baleanu fractional-order derivative is employed to generalize a treatment of the cancer model. This novel type of derivative furnishes us with vital understanding regarding parameters that are widely used in intricate mechanisms. The Picard-Lindelof approach is implemented to investigate the existence and uniqueness of solutions for the fractional cancer treatment system, and Picard's stability approach is used to address governing equations. The findings reveal that the system is more accurate when the fractional derivative is implemented, demonstrating that the behaviour of the cancer treatment can be interpreted when non-local phenomena are included in the system. Furthermore, numerical results for various configurations of the system are provided to exemplify the established simulation.
  • Article
    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) Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; Rashid, Saima
    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.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 10
    Fractional-Order Partial Differential Equations Describing Propagation of Shallow Water Waves Depending on Power and Mittag-Leffier Memory
    (Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; Al Qurashi, Maysaa
    In this research, the (q) over bar -homotopy analysis transform method ((q) over bar -HATM) is employed to identify fractional-order Whitham-Broer-Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of (q) over bar -HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.