Browsing by Author "Ashraf, Rehana"

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Citation Count: Rashid, Saima;...et.al. (2022). "A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise", Results in Physics, Vol.39.
A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise
(2022) Rashid, Saima; Iqbal, Muhammad Kashif; Alshehri, Ahmed M.; Ashraf, Rehana; Jarad, Fahd; 234808
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes newborn immunization via the fractal–fractional (F–F) derivative in the Atangana–Baleanu sense. The population is divided into four groups by this system: susceptibility S(ξ), infectious I(ξ), immunized infants V(ξ), and restored R(ξ). The stochastic technique is used to describe and assess the invariant region, basic reproduction number, and local stability for disease-free equilibrium. This strategy has significant modelling difficulties since it ignores the unpredictability of the system phenomena. To prevent such problems, we convert the deterministic strategy to a randomized one, which seems recognized to have a vital influence by adding an element of authenticity and fractional approach. Owing to the model intricacies, we established the existence-uniqueness of the model and the extinction of infection was carried out. We conducted a number of experimental tests using the F–F derivative approach and obtained some intriguing modelling findings in terms of (i) varying fractional-order (φ) and fixing fractal-dimension (ω), (ii) varying ω and fixing φ, and (iii) varying both φ and ω, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.
Citation Count: Khan, Zareen A...et al. (2020). "Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property", Advances in Difference Equations, Vol. 2020, No. 1.
Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property
(2020) Khan, Zareen A.; Rashid, Saima; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the paper, we extend some previous results dealing with the Hermite–Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Hölder and power-mean inequalities. As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena. © 2020, The Author(s).
Citation Count: Rashid, Saima...et al. (2020). "New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space", Symmetry-Basel, Vol. 12, No. 2.
New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space
(2020) Rashid, Saima; Kalsoom, Humaira; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating PLANCK CONSTANT OVER TWO PI-convex function and predominating quasiconvex function, with respect to eta, are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of eta-convex functions, eta-quasiconvex functions, strongly PLANCK CONSTANT OVER TWO PI-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of kappa-fractional integral operator to generate novel variants related to the Hermite-Hadamard type for pth-order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.
Citation Count: Rashid, Saima...et al. (2020). "New quantum estimates in the setting of fractional calculus theory", Advances in Difference Equations, Vol. 2020, No. 1.
New quantum estimates in the setting of fractional calculus theory
(2020) Rashid, Saima; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this article, the investigation is centered around the quantum estimates by utilizing quantum Hahn integral operator via the quantum shift operator eta psi(q)(zeta) = q zeta + (1 - q)eta, zeta is an element of [mu, nu], eta = mu+ omega/(1-q), 0 < q < 1, omega >= 0. Our strategy includes fractional calculus, Jackson's q-integral, the main ideas of quantum calculus, and a generalization used in the frame of convex functions. We presented, in general, three types of fractional quantum integral inequalities that can be utilized to explain orthogonal polynomials, and exploring some estimation problems with shifting estimations of fractional order e(1) and the q-numbers have yielded fascinating outcomes. As an application viewpoint, an illustrative example shows the effectiveness of q, omega-derivative for boundary value problem.
Citation Count: Rashid, Saima;...et.al. (2022). "Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues", Mathematical Biosciences and Engineering, Vol.19, No.11, pp.11563-11594.
Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues
(2022) Rashid, Saima; Ashraf, Rehana; Asif, Qurat-Ul-Ain; Jarad, Fahd; 234808
In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case’s equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order α and fractal-dimension ℘ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.
Citation Count: Ashraf, Rehana...et al. (2022). "Numerical solutions of fuzzy equal width models via generalized fuzzy fractional derivative operators", AIMS Mathematics, Vol. 7, No. 2, pp. 2695-2728.
Numerical solutions of fuzzy equal width models via generalized fuzzy fractional derivative operators
(2022) Ashraf, Rehana; Rashid, Saima; Jarad, Fahd; Althobaiti, Ali; 234808
The Shehu homotopy perturbation transform method (SHPTM) via fuzziness, which combines the homotopy perturbation method and the Shehu transform, is the subject of this article. With the assistance of fuzzy fractional Caputo and Atangana-Baleanu derivatives operators, the proposed methodology is designed to illustrate the reliability by finding fuzzy fractional equal width (EW), modified equal width (MEW) and variants of modified equal width (VMEW) models with fuzzy initial conditions (ICs). In cold plasma, the proposed model is vital for generating hydromagnetic waves. We investigated SHPTM’s potential to investigate fractional nonlinear systems and demonstrated its superiority over other numerical approaches that are accessible. Another significant aspect of this research is to look at two significant fuzzy fractional models with differing nonlinearities considering fuzzy set theory. Evaluating various implementations verifies the method’s impact, capabilities, and practicality. The level impacts of the parameter ~ and fractional order are graphically and quantitatively presented, demonstrating good agreement between the fuzzy approximate upper and lower bound solutions. The findings are numerically examined to crisp solutions and those produced by other approaches, demonstrating that the proposed method is a handy and astonishingly efficient instrument for solving a wide range of physics and engineering problems.
Citation Count: Rashid, Saima; Ashraf, Rehana; Jarad, F. (2022). "Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels", AIMS Mathematics, Vol.7, No.5, pp.7936-7963.
Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels
(2022) Rashid, Saima; Ashraf, Rehana; Jarad, Fahd; 234808
This 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.