WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
3 results
Search Results
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: 5Citation - Scopus: 7New Applications Related To Hepatitis C Model(Amer inst Mathematical Sciences-aims, 2022) Raza, Ali; Akgul, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd; Ahmed, NaumanThe main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of R-0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R-0 is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if R-0 < 1. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.Article Citation - WoS: 4Citation - Scopus: 5Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Al-Refai, MohammedIn this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.