Browsing by Author "Sultana, Sobia"

Now showing 1 - 6 of 6

Citation - WoS: 7
Citation - Scopus: 9
Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory
(Amer inst Mathematical Sciences-aims, 2022) Al Qurashi, Maysaa; Jarad, Fahd; Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; 234808; Matematik
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.
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.
Citation - WoS: 3
Citation - Scopus: 3
Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling
(Amer inst Mathematical Sciences-aims, 2023) Al-Qurashi, Maysaa; Jarad, Fahd; Sultana, Sobia; Karim, Shazia; Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; 234808; Matematik
Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity over bar R0. The existence and stability of the equilibrium point can be assessed using R over bar 0, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.
Citation - WoS: 9
Citation - Scopus: 9
More efficient estimates via ℏ-discrete fractional calculus theory and applications
(Pergamon-elsevier Science Ltd, 2021) Rashid, Saima; Jarad, Fahd; Sultana, Sobia; Jarad, Fahd; Jafari, Hossein; Hamed, Y. S.; 234808; Matematik
Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. First, we start with a novel discrete h-proportional fractional sum defined on the time scale hZ so as to give the premise to the more broad and complex structures, for example, the suitably accustomed transformations conjuring the property of observing the new chaotic behaviors of the logistic map. Here, we aim to present the novel discrete versions of Gruss and certain other associated variants by employing discrete h-proportional fractional sums are established. Moreover, several novel consequences are recaptured by the h-discrete fractional sums. The present study deals with the modification of Young, weighted-arithmetic and geometric mean formula by taking into account changes in the exponential function in the kernel represented by the parameters of the operator, varying delivery noted outcomes. In addition, two illustrative examples are apprehended to demonstrate the applicability and efficiency of the proposed technique. (C) 2021 Elsevier Ltd. All rights reserved.
Citation - WoS: 20
Citation - Scopus: 20
Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application
(Pergamon-elsevier Science Ltd, 2021) Rashid, Saima; Jarad, Fahd; Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; 234808; Matematik
Discrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain (h) over barZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABTL), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having (h) over bar -discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Polya-Szego and Chebyshev type inequalities introduced within discrete AB-fractional operators having h-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated. (C) 2021 Elsevier Ltd. All rights reserved.
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) Rashid, Saima; Jarad, Fahd; Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y. S.; 234808; Matematik
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.