International Journal of Dynamical Systems and Differential Equations (9 papers in press)

Regular Issues

• Optimal continuous-singular control of stochastic McKean-Vlasov system in Wasserstein space of probability measures.  
  by Samira Boukaf, Lina Guenane, Mokhtar HAFAYED 
  Abstract: In this paper, we study the local form of maximum principle for optimal stochastic continuous-singular control of nonlinear It
  Keywords: Derivative with respect to probability law; Optimal continuous-singular control; McKean-Vlasov stochastic system; Wasserstein space of probability measures.
  
  
• Symmetry analysis of the (3+1) dimensional Kadomtsev-Petviashvilli equation with variable coefficients and an arbitrary nonlinear term  
  by Preeti Devi, Karanjeet Singh 
  Abstract: In this research, the (3+1) dimensional Kadomtsev - Petviashvilli (KP) equation with time dependent variable coefficients and an arbitrary nonlinear term has been investigated by using the classical Lie symmetry approach. A number of governing equations have been worked out to obtain the admissible forms of the arbitrary variable coefficients, in general. To illustrate further the reductions and extraction of the exact solutions, the variable coefficients have been taken, in particular, as power functions of `$t$'. The dimensional reductions of the KP equation have been shown in a systematic manner, leading eventually to nonlinear ordinary differential equations (ODEs). The solutions to these nonlinear ODEs have been furnished, wherever non-trivial Lie symmetries were admitted, and derivation of the exact solution was possible.
  Keywords: Lie symmetry; (3+1) dimensional KP equation; Exact solutions.
  
  
• On the Existence and Uniqueness Results for Intuitionistic Fuzzy Partial Differential Equations  
  by Bouchra Ben Amma, Said Melliani, Lalla Saadia Chadli 
  Abstract: In this work, we have investigated the issue of the existence and uniqueness of intuitionistic fuzzy solutions for partial differential equations with local and nonlocal initial conditions using the Banach fixed point theorem based on a new complete intuitionistic fuzzy metric space. In addition, we have presented a method of steps to solve intuitionistic fuzzy partial differential equations. A computational example for our results is given with some numerical simulations of the solutions.
  Keywords: Partial Differential Equations; Local and Nonlocal conditions; Intuitionistic Fuzzy Solutions.
  
  
• Dynamic output-feedback $H_infty$ control for TS fuzzy systems with probabilistic faults and time-varying input delay  
  by Mohanapriya Rajagopal, Dhanalakshmi Palanisamy, Senpagam Sundarrajan 
  Abstract: This paper develops a new fuzzy Dynamic Output-Feedback controller for TS fuzzy systems with probabilistic actuator faults and time-varying input delay. The central sight is to consider the bounded H? performance by the influence of stochastic faults which is modeled by introducing Bernoulli distributed sequences. The novel stability criterion is established to guarantee the stochastic stabilization of the resultant closed-loop system and satisfies a prescribed performance by implementing Lyapunov-Krasovskiis functional approach. Furthermore, the gain values of the controller are calculated by solving a set of LMIs. Eventually, analytical example is provided to demonstrate the merits and applicability of the prospective method.
  Keywords: TS fuzzy control systems; stochastic fault; Dynamic Output-Feedback control; time-varying delay; control input.
  
  
• Uniqueness and Ulam Stability for Implicit Fractional q-Difference Equations via Picard Operators Theory  
  by Said Abbas, Mouffak Benchohra, John Graef, Nadjet Laled 
  Abstract: The authors are concerned with the uniqueness of solutions and Ulam type stability results for implicit Caputo fractional q-difference equations. Coupled systems of implicit fractional q-difference equations are also considered. Their results are obtained by using the Picard operator theory due to Rus. An illus- trative example is given in the last section of the paper.
  Keywords: Fractional q-difference equation; coupled system; implicit; weekly Picard operator; fixed point equation; Ulam-Hyers-Rassias stability; fixed point.
  
  
• Stability analysis of a delay differential equation describing antiviral immune response  
  by Fatima Boudchich, Jaafar El Karkri, Rajae Aboulaich 
  Abstract: The aim of this work is to study the dynamics of viral infection by a mathematical model using a differential equation with a single delay corresponding to the duration of proliferation and differentiation of immune cells and the time required to program activated CTLs. Asymptotic and global stability conditions for the considered delayed differential equation are defined in order to study the asymptotic behavior of the solutions. Key theorems are proven using the theory of monotone dynamical systems, mainly the results established by Mr. Pituk in 2003. Sufficient conditions for the stability of the non-zero equilibrium have been established and formulated in terms of efficacy and delay of the immune response. Sufficient conditions of stability of the nonzero equilibrium have been established and formulated in terms of the efficiency and the delay of the immune response. Numerical simulations of the model are given to validate analytical results.
  Keywords: Immune response models; Differential equations with single delay; Global asymptotic stability; Monotone semi-flows.
  
  
• Further results on dynamical properties for a fractional-order predator-prey model  
  by Yizhong Liu 
  Abstract: On the basis of previous studies, we set up a new fractional-order predator-prey model.\r\nFirst, by basic theory of algebraic equation, we discuss the existence of equilibrium point.\r\n Second, with the help of Lipschitz condition, we discuss the existence and uniqueness of solution. Third,\r\napplying the derivative theory of functions, we prove the non-negativity of solution. Fourth, using the inequality technique of fractional-order differential equations,\r\nwe obtain the sufficient condition to ensure the uniformly boundedness of solution. Fifth, by analyzing the Jacobian matrix, the locally asymptotically stability of the equilibria has been\r\ninvestigated; By constructing some suitable Lyapunov functions,\r\nthe globally asymptotically stability of the equilibria bas been analyzed. Sixth, the computer simulation diagrams are displayed to illustrate the correctness of the\r\nanalytic findings. Finally, a concise conclusion is give to end this article.
  Keywords: Fractional-order predator-prey model; existence and uniqueness;\r\n non-negative; boundedness; stability; global asymptotic stability.
  
  
• Stability and Hopf Bifurcation Analysis of a delayed SIRC Epidemic Model for Covid-19  
  by Geethamalini Shankar, Venkataraman Prabhu 
  Abstract: This paper examines the spread of the Coronavirus Diseases 2019 (COVID-19) pandemic using the SIRC epidemic model with transmission delay. We investigate the impact of time lag on stability of steady state. We obtain the local stability of the infection-free steady state and infected steady state. The length of delay that must be estimated in order to sustain stability has rnbeen calculated. The Hopf bifurcation is used to explain the nature of the disease at the onset of a second cycle, as well as the types of treatment measures that would be required to curtail it. We show that the infected steady state is asymptotically stable locally in the presence of delays and that when ? crosses a critical value, a Hopf bifurcation occurs by using the transmission rndelay ? as a bifurcation parameter. Theoretical results are supported through numerical rnsimulations.rn
  Keywords: Bifurcation; COVID-19; Cross-immunity; SIRC model; Stability.
  
  
• Steady-State Solution for Discrete Oort-Hulst-Safronov Coagulation Equation  
  by Sonali Kaushik, Rajesh Kumar 
  Abstract: The article examines the steady-state behavior of the Safronov-Dubovski coagulation equation for the kernel $V_{i,j}=C_V(i^{beta}j^{gamma}+,i^{gamma}j^{beta}) hspace{.1 cm}$ when $0 leq beta leq gamma leq 1, hspace{.1 cm} (,beta+gamma,) in [0,2] hspace{.1 cm} forall hspace{.1 cm} i,j in mathbb{N}, hspace{.1 cm} C_V in mathbb{R}^{+}$. By assuming the boundedness of the second moment, the existence of a unique steady-state solution is established. Since, the model is non-linear and analytical solutions are not available for such cases, numerical simulations are performed to justify the theoretical findings. Four different test cases are considered by taking physically relevant kernels such as $V_{i,j}=2, (i+j), 8i^{1/2}j^{1/2} hspace{.1 cm} text{and} hspace{.1 cm} 2ij$ along with various initial conditions. The obtained results are reported in the form of graphs and tables.
  Keywords: Safronov-Dubovski Coagulation; Existence; Uniqueness; Steady-State Solution; Moments.