Browsing by Author "Safdar, Farhat"

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Citation Count: Qurashi, Maysaa Al;...et.al. (2023). "New numerical dynamics of the fractional monkeypox virus model transmission pertaining to nonsingular kernels", Mathematical Biosciences and Engineering, Vol.20, No.1, pp.402-436.
New numerical dynamics of the fractional monkeypox virus model transmission pertaining to nonsingular kernels
(2023) Qurashi, Maysaa Al; Rashid, Saima; Alshehri, Ahmed M.; Jarad, Fahd; Safdar, Farhat; 234808
Monkeypox (MPX) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system’s equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system’s disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus’s transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.
Citation Count: Rashid, Saima...et al. (2020). "On Polya-Szego Type Inequalities via K-Fractional Conformable Integrals", Punjab University Journal of Mathematics, Vol. 52, no. 5, pp. 63-76.
On Polya-Szego Type Inequalities via K-Fractional Conformable Integrals
(2020) Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat; 234808
The studies of inequalities regarding the fractional differential and integral operators are considered to be essential because of their potential applications among researchers. This paper consigns to the generalizations of novel fractional integral inequalities. The Polya-Szego type variants are generalized by involving K-fractional conformable integrals (KFCI): This is the K-analogue of the fractional conformable integrals. We discuss the implications and other consequences of the K-fractional conformable fractional integrals.
Citation Count: Kalsoom, Humaira...et al. (2020). "Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings", Symmetry-Basel, Vol. 12, No. 3.
Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings
(2020) Kalsoom, Humaira; Rashid, Saima; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Akram, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389
By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard's type inequality and conclude explicit bounds for two new definitions of (p(1)p(2), q(1)q(2))-differentiable function and (p(1)p(2), q(1)q(2))-integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for (p(1)p(2), q(1)q(2))-integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for (p(1)p(2), q(1)q(2))-differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.
Citation Count: Chu, Hong-Hu...et al. (2020). "Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function correlated with Coordinated Generalized phi-Convex Functions", Symmetry-Basel, Vol. 12, No. 2.
Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function correlated with Coordinated Generalized phi-Convex Functions
(2020) Chu, Hong-Hu; Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Chu, Yu-Min; Baleanu, Dumitru; 56389
In this paper, the newly proposed concept of Raina's function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag-Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q1q2-differentiable function by inserting Raina's functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized phi-convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina's function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.