The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have ...The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.展开更多
Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower ...Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.展开更多
In this paper,we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission.The existence and uniqueness,nonnegativity and finiteness of solutions for our suggested...In this paper,we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission.The existence and uniqueness,nonnegativity and finiteness of solutions for our suggested model have been studied.Different equilibria of the model are found and their local and global stability analyses are also examined.Furthermore,the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model.We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation.We have demonstrated the analytical results of our proposed model system through several numerical simulations.展开更多
基金The Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia has funded this project under Grant Number(G:220-247-1443).
文摘The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.
基金supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT-Fundação para a Ciência e a Tecnologia),within project UIDB/04106/2020Fund Scientific Research MU21FMI007,University of Plovdiv"Paisii Hilendarski".
文摘Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.
基金The work of S.J.is financially supported by the Department of Science&Technology and Biotechnology,Government of West Bengal(vide memo no.201(Sanc.)/ST/P/S&T/16G-12/2018 dt 19-02-2019)。
文摘In this paper,we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission.The existence and uniqueness,nonnegativity and finiteness of solutions for our suggested model have been studied.Different equilibria of the model are found and their local and global stability analyses are also examined.Furthermore,the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model.We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation.We have demonstrated the analytical results of our proposed model system through several numerical simulations.
