Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 22Citation - Scopus: 26Impact of Public Health Awareness Programs on Covid-19 Dynamics: a Fractional Modeling Approach(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Musa, Salihu s.; Qureshi, Sania; Alshomrani, Ali s.; Baleanu, Dumitru; Zafar, Zain ul abadinPublic health awareness programs have been a crucial strategy in mitigating the spread of emerging and re-emerging infectious disease outbreaks of public health significance such as COVID-19. This study adopts an Susceptible-Exposed-Infected-Recovered (SEIR) based model to assess the impact of public health awareness programs in mitigating the extent of the COVID-19 pandemic. The proposed model, which incorporates public health awareness programs, uses ABC fractional operator approach to study and analyze the transmission dynamics of SARS-CoV-2. It is possible to completely understand the dynamics of the model's features because of the memory effect and hereditary qualities that exist in the fractional version. The fixed point theorem has been used to prove the presence of a unique solution, as well as the stability analysis of the model. The nonlinear least-squares method is used to estimate the parameters of the model based on the daily cumulative cases of the COVID-19 pandemic in Nigeria from March 29 to June 12, 2020. Through the use of simulations, the model's best-suited parameters and the optimal ABC fractional-order parameter t may be determined and optimized. The suggested model is proved to understand the virus's dynamical behavior better than the integer-order version. In addition, numerous numerical simulations are run using an efficient numerical approach to provide further insight into the model's features.Article Citation - WoS: 4Citation - Scopus: 4Nonlinear Wave Train in an Inhomogeneous Medium With the Fractional Theory in a Plane Self-Focusing(Amer inst Mathematical Sciences-aims, 2022) Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; Asjad, Muhammad ImranThe aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional beta differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and beta fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and beta-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.Article Citation - WoS: 22Citation - Scopus: 22Lump Collision Phenomena To a Nonlinear Physical Model in Coastal Engineering(Mdpi, 2022) Yusuf, Abdullahi; Alshomrani, Ali Saleh; Baleanu, Dumitru; Sulaiman, Tukur AbdulkadirIn this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has not yet been explored due to its vital physical significant in various field of nonlinear science. In order to establish some more interaction solutions with some novel physical features, we establish collision aspects between lumps and other solutions by using trigonometric, hyperbolic, and exponential functions. The obtained novel types of results for the governing equation includes lump-periodic, two wave, and breather wave solutions. Meanwhile, the figures for these results are graphed. The propagation features of the derived results are depicted. The results reveal that the appropriate physical quantities and attributes of nonlinear waves are related to the parameter values.Article Citation - WoS: 9Citation - Scopus: 12Two-Wave, Breather Wave Solutions and Stability Analysis To the (2+1)-Dimensional Ito Equation(Elsevier, 2022) Yusuf, Abdullahi; Hincal, Evren; Baleanu, Dumitru; Bayram, Mustafa; Sulaiman, Tukur AbdulkadirThe current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed phys-ical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study's findings may help explain the physics behind some of the chal-lenges facing ocean engineers.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )Article Citation - WoS: 37Citation - Scopus: 43New Solitary Wave Solutions and Stability Analysis of the Benney-Luke and the Phi-4 Equations in Mathematical Physics(Amer inst Mathematical Sciences-aims, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Ghanbari, BehzadIn this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.Article Citation - WoS: 14Citation - Scopus: 15Lump, Its Interaction Phenomena and Conservation Laws To a Nonlinear Mathematical Model(Elsevier, 2022) Sulaiman, Tukur Abdulkadir; Hincal, Evren; Baleanu, Dumitru; Yusuf, AbdullahiWe solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation. Some unique interaction phenomena have been obtained between lump so-lution, breather wave, periodic wave, kink soliton, and two-wave solutions. All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12. The physical characteristics of the solutions have been visually represented to shed additional light on the acquired re-sults. Furthermore, using the novel conservation theory, the conserved vectors of the governing equation have been generated. The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )Article Citation - WoS: 8Analysis of Meningitis Model: a Case Study of Northern Nigeria(Amer inst Mathematical Sciences-aims, 2020) Olamilekan, Lawal Ibrahim; Yusuf, Abdullahi; Baleanu, Dumitru; Baba, Isa AbdullahiA new strain of meningitis emerges in northern Nigeria, which brought a lot of confusion. This is because vaccine and treatment for the old strain was adopted but to no avail. It was later discovered that it was a new strain that emerged. In this paper we consider the two strains of meningitis (I 1 and I 2). Our aim is to analyse the effect of one strain on the dynamics of the other strain mathematically. Equilibrium solutions were obtained and their global stability was analysed using Lyaponuv function. It was shown that the stability depends on magnitude of the basic reproduction ratio. The coexistence of the two strains was numerically shown.Article Citation - WoS: 9Citation - Scopus: 10Optical Solitons and Modulation Instability Analysis To the Quadratic-Cubic Nonlinear Schrodinger Equation(inst Mathematics & informatics, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrodinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.Article Citation - WoS: 3Citation - Scopus: 6Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaThis paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.Article Citation - WoS: 2Citation - Scopus: 2Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu IsaIn this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.