Browsing by Author "Akram, Saima"

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Citation Count: Ghaffar, Abdul...et al. (2020). "A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order", Advances in Difference Equations, Vol. 2020, No. 1.
A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order
(2020) Ghaffar, Abdul; Ali, Ayyaz; Ahmed, Sarfaraz; Akram, Saima; Junjua, Moin-ud-Din; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
We investigate some solitary wave results of time fractional evolution equations. By employing the extended rationalexp((-psi '/psi)(eta))-expansion method, a few different results including kink, singular-kink, multiple soliton, and periodic wave solutions are formally generated. It is worth mentioning that the solutions obtained are more general with more parameters. The exact solutions are constructed in the form of exponential, trigonometric, rational, and hyperbolic functions. With the choice of proper values of parameters, graphs to some of the obtained solutions are drawn. On comparing some special cases, our solutions are in good agreement with the results published previously and the remaining are new.
Citation Count: Ashraf, P...et al. (2020). "Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations",Mathematics, Vol. 8, No. 3.
Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme
(MDPI AG, 2020) Pakeeza, Ashraf; Bushra, Nawaz,; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Ahmed Khan, Muhammad Aqeel; Akram, Saima; 56389
Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation.
Citation Count: Akram, Saima...et al. (2020). "Periodic Solutions of Some Classes of One Dimensional Non-autonomous Equation", Frontiers in Physics, Vol. 8.
Periodic Solutions of Some Classes of One Dimensional Non-autonomous Equation
(2020) Akram, Saima; Nawaz, Allah; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, the periodic solutions of a certain one-dimensional differential equation are investigated for the first order cubic non-autonomous equation. The method used here is the bifurcation of periodic solutions from a fine focus z = 0. We aimed to find the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. For classes C3, 8, C4, 3, C7, 5, C7, 6, eight periodic multiplicities have been found. To investigate the multiplicity >9, the formula for the focal value was not available in the literature. We also succeeded in constructing the formula for η10. By implementing our newly developed formula, we are able to get multiplicity ten for classes C7, 3, C9, 1, which is the highest known to date. A perturbation method has been properly established for making the maximal number of limit cycles for each class. Some examples are also presented to show the implementation of the newly developed method. By considering all of these facts, it can be concluded that the presented methods are new, authentic, and novel.
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: Akram, Saima...et al. (2020). "Standard routine techniques of modeling of tick-borne encephalitis", Open Physics, Vol. 18, No. 1, pp. 820-828.
Standard routine techniques of modeling of tick-borne encephalitis
(2020) Akram, Saima; Arooj, Aroosa; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; 56389
Tick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R 0-like threshold has been derived by using the next-generation matrix method. The formula for R 0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.