Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel cha...Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.展开更多
This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discon...This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.展开更多
DESIGN:Please introduce the special charm of Elica design to our readers. Fabrizio Crisa:In Elica cooker hoods: charm is generated by the sense of wellbeing which we hope the users can feel using our products;I love t...DESIGN:Please introduce the special charm of Elica design to our readers. Fabrizio Crisa:In Elica cooker hoods: charm is generated by the sense of wellbeing which we hope the users can feel using our products;I love to think the design such as way to improve daily life. Thanks to the design of our cooker hoods we spread the importance of the air.As our last advertising campaign explains: "Air is precious.Do not waste it".We hardly believe in this.展开更多
In this paper,we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method(q-HATM)with the fractional operator.The analyz...In this paper,we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method(q-HATM)with the fractional operator.The analyzed model consists of a system of three nonlinear differential equations elucidating the activation and the migratory response of the degradation of the matrix,tumour cells and production of degradative enzymes by the tumour cells.The considered method is graceful amalgamations of q-homotopy analysis technique with Laplace transform(LT),and Caputo–Fabrizio(CF)fractional operator is hired in the present study.By using the fixed point theory,existence and uniqueness are demonstrated.To validate and present the effectiveness of the considered algorithm,we analyzed the considered system in terms of fractional order with time and space.The error analysis of the considered scheme is illustrated.The variations with small change time with respect to achieved results are effectively captured in plots.The obtained results confirm that the considered method is very efficient and highly methodical to analyze the behaviors of the system of fractional order differential equations.展开更多
In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and th...In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative.We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model.Then,we study the global asymptotic stability of disease-free equilibrium of the fractional models.We also prove,for each fractional model,the existence and uniqueness of solutions.An iterative solution of the two models is computed using the Predictor–Corrector method.Using realistic parameter values,we perform numerical simulations for different values of the fractional order.Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.展开更多
文摘Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.
文摘This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.
文摘DESIGN:Please introduce the special charm of Elica design to our readers. Fabrizio Crisa:In Elica cooker hoods: charm is generated by the sense of wellbeing which we hope the users can feel using our products;I love to think the design such as way to improve daily life. Thanks to the design of our cooker hoods we spread the importance of the air.As our last advertising campaign explains: "Air is precious.Do not waste it".We hardly believe in this.
文摘In this paper,we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method(q-HATM)with the fractional operator.The analyzed model consists of a system of three nonlinear differential equations elucidating the activation and the migratory response of the degradation of the matrix,tumour cells and production of degradative enzymes by the tumour cells.The considered method is graceful amalgamations of q-homotopy analysis technique with Laplace transform(LT),and Caputo–Fabrizio(CF)fractional operator is hired in the present study.By using the fixed point theory,existence and uniqueness are demonstrated.To validate and present the effectiveness of the considered algorithm,we analyzed the considered system in terms of fractional order with time and space.The error analysis of the considered scheme is illustrated.The variations with small change time with respect to achieved results are effectively captured in plots.The obtained results confirm that the considered method is very efficient and highly methodical to analyze the behaviors of the system of fractional order differential equations.
文摘In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative.We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model.Then,we study the global asymptotic stability of disease-free equilibrium of the fractional models.We also prove,for each fractional model,the existence and uniqueness of solutions.An iterative solution of the two models is computed using the Predictor–Corrector method.Using realistic parameter values,we perform numerical simulations for different values of the fractional order.Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.
