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International Journal of Dynamical Systems and Differential Equations

International Journal of Dynamical Systems and Differential Equations (IJDSDE)

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International Journal of Dynamical Systems and Differential Equations (27 papers in press)

Regular Issues

  • Existence and Boundary Behavior of Positive Solutions for a Coupled Fractional System   Order a copy of this article
    by Imen Ben Saad, Sameh Turki, Zagharide Zine El Abidine 
    Abstract: We consider the following semilinear fractional system begin{equation*} label{eq1} left{ begin{array}{ll} displaystyle D^{alpha} u=p(t)displaystyle u^{a}displaystyle v^{r}textrm{ in }(0,1) , displaystyle D^{beta} v=q(t)displaystyle u^{s }displaystyle v^{b}textrm{ in }(0,1) , displaystylelim_{t rightarrow 0^{+}}displaystyle t^{1-alpha}u(t) =displaystylelim_{t rightarrow 0^{+}} displaystyle t^{1-beta}v(t)=0, end{array} right. end{equation*}% where $ alpha, ; betain (0,1)$, $a,; b in(-1,1)$, $r, ;sinmathbb{R}$ such that $(1-'a')(1-'b')-'rs'>0$, $D^{alpha}$, $D^{beta}$ are the Riemann-Liouville fractional derivatives of orders $alpha, ; beta$ and the nonlinearities $p, ; q$ are positive measurable functions on $(0, 1)$. Applying the Sch"{a}uder fixed point theorem, we establish the existence and the boundary behavior of positive solutions in the space of weighted continuous functions.
    Keywords: System of fractional differential equations; Boundary behavior; Karamata class; Schauder's fixed point theorem.

  • Analysis on product graphs along with the utilization of Restrained step triple connected domination parameter   Order a copy of this article
    by Mahadevan G, Vimala Suganthi M, Iravithul Basira A 
    Abstract: Recently, author's introduced the concept of restrained step triple connected domination number. In this paper we analysis general results for the strong product of paths and cycles along with application of restrained step triple connected domination number of a graph with reality.
    Keywords: Restrained domination number; triple connected domination number; Restrained step domination; rstc-number.

  • A constructive approach to degenerate center problem   Order a copy of this article
    by Mahdieh Molaei Derakhtenjani, Omid Rabiei Motlagh, Haji Mohammad Mohammadi Nejad 
    Abstract: We give a constructive approach to the degenerate center problem?. ?First?, ?we consider homogeneous polynomial systems and provide various conditions for which the origin is a center?. ?Then?, ?by using the Poincare coefficients in polar coordinate?, ?we complete a rigorous computation such that the nonhomogeneous system perturbed by lower terms has an annular region surrounding the origin?. ?This enables us to show that a degenerate center may be the limit of a linear center?, ?a nilpotent singularity?, ?and even a hyperbolic saddle point?. ?Finally?, ?we provide sufficient conditions such that the origin is a degenerate center for a nonhomogeneous system?. ?The system may be of even degree?, ?so we have degenerate centers of even degree?, ?which are rare?.
    Keywords: Center Problem; Degenerate Center; Perturbation of Poincare Map.
    DOI: 10.1504/IJDSDE.2022.10041165
  • Analysis of Brain Tumor Growth Model by Adomian Decomposition Method   Order a copy of this article
    by Archana Varsoliwala, Twinkle Singh 
    Abstract: The current work involves the study of brain tumor growth (glioblastoma), which is a very aggressive brain tumor. The mathematical model is mainly based on two parameters - the diffusion and growth of tumor cells. Based on various medical studies conducted by researchers, which demonstrate that the combination of radiotherapy and chemotherapy can lead to negative tumor growth. This study uses the Adomian Decomposition Method and its convergence analysis to obtain an approximate solution of equation governing tumor growth. The result is consistent with the physical phenomenon of tumor growth, in which tumor concentration increases linearly after a patient is treated with combination therapy as opposed to rapid exponential growth.
    Keywords: Adomian Decomposition Method; Burgess equation; Adomian polynomials; Non-linear partial differential equation.

  • Optimal continuous-singular control of stochastic McKean-Vlasov system in Wasserstein space of probability measures.   Order a copy of this article
    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.

  • Non-uniqueness of solution for initial value problem of impulsive fractional partial differential equations   Order a copy of this article
    by Xian-Min Zhang 
    Abstract: This paper mainly researches the formulas of solution for the initial value problems (IVPs) of two impulsive fractional partial differential equations (IFrPDEs). For these IVPs of IFrPDEs, some properties of their solutions are found, which uncover that the formulas of solution given by some cited papers are inappropriate due to not meeting these properties. Next, by analyzing errors between the approximate solutions and exact solutions, two new formulas of solution of these IVPs of IFrPDEs are discovered that are the integral equations with some undetermined differentiable functions, which illustrate the non-uniqueness of solution of the IVPs of IFrPDEs to be expounded by two examples.
    Keywords: fractional partial differential equations; impulsive fractional partial differential equations; impulse;initial value problems; non-uniqueness of solution.

    by Bharadwaj BVK, Pallav Baruah 
    Abstract: In this paper we have considered a generalized coupled system of nonlinear ordinary differential equations involving derivative terms. We have given sufficient conditions on the nonlinear functions such that the solutions pair asymptotically behaves like a pair of real polynomials.
    Keywords: Non-linear Coupled Ordinary Differential Equations; Fixed-point Theorem; Asymptotically Polynomial like solutions.

  • Time optimal control for an epidemic system with isolation and quadratic treatment   Order a copy of this article
    by Soovoojeet Jana, Anupam Khatua, Tapan Kumar Kar, Manotosh Mandal 
    Abstract: The main objective of this article is to explore the use of time optimal control problem to eradicate epidemic diseases. In the first part, an SIS type epidemic model with isolation and quadratic treatment control is proposed. Then the local and global dynamics of the system is studied. Next in the second part, a time optimal control problem is formulated in order to reach the disease free state in a minimum possible time. By means of Pontryagin's maximum principle, the optimal control problem is solved and the explicit expression of the optimal time is derived for the developed model system.
    Keywords: Epidemic model; isolation; quadratic treatment; global stability; time optimal control.

  • Oscillation and Disconjugacy for Generalized Half-Linear Differential Equations with Bohr Almost Periodic Coefficients   Order a copy of this article
    by Mohammad MOALLA, Sami INJROU, Ramez KARROUM 
    Abstract: This study aims to examine the disconjugacy and the oscillation domain of the generalized half-linear second order differential equations with almost periodic coefficients in the sense of Bohr. Some properties of topological D (the disconjugacy domain) and O (the oscillation domain) are identified, and the boundary of D is also studied.
    Keywords: half-linear; disconjugacy; oscillation; almost periodic coefficients; Riccati transformation.

  • A Model for the population dynamics of banana weevil, Cosmopolites sordidus (Germar) with harvesting and time delay: implications for management   Order a copy of this article
    by Eliab Horub Kweyunga, Julius Tumwiine, Eldad B. Karamura 
    Abstract: In this paper, we study a single species logistic delayed model to represent the dynamics of the banana weevil Cosmopolites sordidus (Germar) population. In particular, we consider a logistic equation that incorporates time delay in the recruitment term and constant effort trapping. We analyse the model for the existence and stability of the steady states. The effects of time delay and constant effort trapping on the dynamics of the banana weevil population are investigated. We validate our analytical results using numerical simulations for a given set of parameter values and find that a reduction in egg-to-adult banana weevil survival rate coupled with early and constant effort trapping of the banana weevils are key in management of infestation of the banana plantation.
    Keywords: asymptotic stability; banana weevil; transcritical bifurcation; logistic delayed differential equation; time delay; constant effort harvesting.

  • Harmless Off-Diagonal Delays in Delay Differential Equations   Order a copy of this article
    Abstract: Systems of linear differential equations with delays in the off-diagonal entries and constant coefficients are considered. Sufficient conditions for the delays to be harmless and for the preservation of instability are obtained. This is applied to systems of two preys and two mutualistic predators with time delays due to gestation, and a time delay model with increasing returns.
    Keywords: time delays; harmless delays; mutualism.

  • Approximate Controllability of Sobolev-Type Nonlocal Hilfer Fractional Stochastic Differential System   Order a copy of this article
    by Saravanakumar Subramaniam 
    Abstract: This manuscript is concerned with the approximate controllability of Sobolevtype nonlocal Hilfer fractional stochastic differential system driven by fractional Brownianrnmotion (fBm) and Poisson jumps. By utilizing the concepts of fractional calculus, stochasticrntheory, semi group theory, we prove the required conditions by assuming that the linearrnsystem is approximately controllable. Schauders fixed point theorem is used to derive thernnecessary result. Further, an example is provided to express the obtained theoretical result
    Keywords: Approximate controllability; Hilfer fractional derivative; Stochastic differential system; Nonlocal condition; Rosenblatt Process.

  • Singular boundary value problem for fractional q-difference equations with a parameter   Order a copy of this article
    by Lulu Zhang, Shurong Sun 
    Abstract: In this paper, we study a class of singular boundary value problem for fractional q-difference equations involving Caputo derivatives subject to Sturm-Liouville boundary conditions.rn By using Krasnoselskii fixed point theorem, the existence of solutions in term of parameter is considered.
    Keywords: fractional q-difference equations; singular; boundary value problem.

  • Dynamics analysis of modified Leslie-Gower prey-predator system with Holling type II functional response   Order a copy of this article
    Abstract: In this paper, we investigate a modified Leslie-Gower prey-predator system with Holling type II functional response. For the non-spatial system, we studied the stability of coexisting homogeneous steady-states. Further, we examined the occurrence of Hopf bifurcation at non-trivial equilibrium and the stability of bifurcate periodic solutions. In addition, we analyzed the existence of diffusion-driven instability of equilibrium solution. Moreover, we derived some conditions regarding parameters to establish the existence of Turing instability. Also, numerical simulations are carried out to verify our analytical results.
    Keywords: Prey-Predator System; Stability; Hopf Bifurcation; Periodic Solutions; Turing Instability; Diffusion.

  • An Application of Nonlinear Integro-differential Equations by Differential Transform Method with Adomian Polynomials   Order a copy of this article
    by Xuchao Bao, Yue Chan 
    Abstract: In this paper, we introduce the modified DTM (MDTM), where the nonlinear terms in nonlinear integro-differential equations are replaced by Adomian polynomials so as to make the Differential Transform Method (DTM) more efficient to compute. We provide a simple numerical example to illustrate its application. The modified method is also used to solve a nonlinear dynamic system problem of spherical robots.
    Keywords: Adomian polynomials; nonlinear integro-differential equations; DTM.

  • Oscillation of second-order nonlinear delay dynamic equations on time scales with a nonpositive neutral term   Order a copy of this article
    by Hassan Agwa, Ahmed Khodier, Mahmoud Hamam 
    Abstract: In this paper, we establish some new oscillation criteria for second-order nonlinear neutral delay dynamic equation with nonpositive neutral term on a time scale T. The obtained results not only generalize and extend some existing results but also can be applied to some of the oscillation problems that are not covered before. Finally, we give an example to illustrate our main results.
    Keywords: Oscillation; Neutral equation; Delay equation; Dynamic equation; Time scale.

  • Dynamic behavior of a predator-prey system with impulsive control strategy   Order a copy of this article
    by Tian Baodan, Li Jiamei, Wu Xue, Zhang Yong 
    Abstract: In this paper, a class of predator-prey system with Beddington-DeAngelis functional response and Allee effect is studied, where impulsive effects are also considered in the model. By using small parameters perturbation skills, comparison theorem and Floquet theory for the impulsive equations, the globally asymptotical stability of the prey-eradication periodic solution and the persistence for the system are obtained. Finally, some numerical examples and simulations are presented by Matlab software to support the theoretical results. The influence of impulsive perturbation intensity and impulsive period on the persistence and periodic solution of the system are discussed.
    Keywords: Impulsive effects; Floquet theory; Permanence; Periodic solution; Globally asymptotical stability.

  • Synchronization of fractional dynamical chaotic systems with several slaves   Order a copy of this article
    by Mohsen Farmani Ardehaei, Mohammad Hadi Farahi, Sohrab Effati 
    Abstract: In this paper, a synchronization of dynamical chaotic systems in fractional order using active control is considered. A novel back-stepping approach is proposed to design an active control and a Lyapunov function. This method is an approach that interlaces the design of active control with the choice of a Lyapunov function. Based on stability theorems in fractional calculus, analysis of stability is performed for the proposed method. Numerical results illustrate the effectiveness of the method.
    Keywords: Synchronization; Chaotic systems; Fractional calculus; Chaotic synchronization; Lyapunov function,Stability; Active control.

  • A comparative simulation and experimental study for control of a ball and plate system using model-based controllers   Order a copy of this article
    by Firas Haddad, Jasem Tamimi 
    Abstract: A ball and plate system (BPS) is a standard system case study in the control engineering which is known as a nonlinear, a multivariable and an unstable system, has been widely used to investigate and demonstrate new control strategies that can deal with nonlinearities. In this paper, five control strategies are applied to control and stabilise a lab-made BPS prototype, particularly, linear model predictive control (LMPC), proportional-integral-derivative (PID), state feedback using pole placement, linear quadratic regulator (LQR) and linear quadratic tracker (LQT) controllers. These controllers have been simulated using MATLAB environment and then implemented using the Arduino Uno ATmega328P microcontroller. Therefore, MATLAB program is also used to evaluate the closed loop system responses and to determine the parameters and the gains for different controllers in a real-time fashion. Finally, a comparison as well as a superiority conclusions are presented for the used controllers for this BPS.
    Keywords: ball and plate; linear quadratic tracker; model predictive control.
    DOI: 10.1504/IJMRS.2022.10044023
  • Solvability and conservation laws of a generalized time-fractional wave-diffusion equations via invariant analysis   Order a copy of this article
    by Youwei Zhang 
    Abstract: In this paper, invariant analysis of a generalized time-fractional wave-diffusion equation in sense of the modified Riemann-Liouville derivative is considered. Differential invariant properties of the admitted Lie groups are used to reducing order in given wave-diffusion equation, geometric vector fields and exact solutions are obtained. The derivation of conservation laws associated with the invariant analysis of the equation are constructed by the Noether's theorem.
    Keywords: Wave-diffusion; Erd'{e}lyi-Kober operator; symmetry reductions; exact solution; conservation laws.

  • Symmetry analysis of the (3+1) dimensional Kadomtsev-Petviashvilli equation with variable coefficients and an arbitrary nonlinear term   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.

  • Role of nutritional food value and Allee effect in controlling chaos in a tri-trophic food chain with omnivory nature of top-predator   Order a copy of this article
    by Krishna Pada Das, Kulbhushan Agnihotri, Harpreet Kaur, Sunil Kumar 
    Abstract: In this paper, a tri-trophic food chain mathematical model is suggested and examined to explore its dynamical behaviour by considering Allee effect in prey population and omnivory behaviour of the top predator i.e. its potential to feed on more than one trophic level. Conditions for local stability of the non-zero equilibrium point are found. The persistence of the system is also discussed. Evolution of chaos from a stable focus is found through numerical simulations when the half-saturation parameter is increased. It is also established that the omnivory and Allee parameters help to restrain the chaotic dynamics.
    Keywords: Food chain; Hopf bifurcation; Local stability; Nutrition; Permanence; Chaos; Omnivory; Allee effect.

  • Further results on dynamical properties for a fractional-order predator-prey model   Order a copy of this article
    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.