Vol. 13, No. 1 (2024): Regular Issue

This paper applies reliability analysis to the fuel control system of an airplane. The rates of transition to fail states follow exponential distributions. Two types of repair are compared, with the Gumbel-Hougaard copula yielding higher profits under our model. General repair is sufficient while a system is working in a degraded state. However, if the system is fully failing, copula distribution should be used for quick system maintenance. Reliability indicators are computed over time, including availability, mean time to failure, and sensitivity. To develop explicit formulations for profit, mean time to failure, and steady-state availability, differential difference equations are constructed and resolved. The system is solved using a supplementary variable technique. Numerical results were generated using the Mathematica software.

This paper applies reliability analysis to the fuel control system of an airplane. The rates of transition to fail states follow exponential distributions. Two types of repair are compared, with the Gumbel-Hougaard copula yielding higher profits under our model. General repair is sufficient while a system is working in a degraded state. However, if the system is fully failing, copula distribution should be used for quick system maintenance. Reliability indicators are computed over time, including availability, mean time to failure, and sensitivity. To develop explicit formulations for profit, mean time to failure, and steady-state availability, differential difference equations are constructed and resolved. The system is solved using a supplementary variable technique. Numerical results were generated using the Mathematica software.

Using the fundamentals of functional differential equations, we provide explicit controllability results for a family of semilinear nonautonomous predator-prey systems in this study. The suggested method is simple in terms of hefty estimations as compared to standard ways because it avoids the well-known fixed point theory approach. It's also effective because it doesn't require any of the unnatural conditions that fixed point theory requires. Finally, we looked at a case study with simulation findings.

Using the fundamentals of functional differential equations, we provide explicit controllability results for a family of semilinear nonautonomous predator-prey systems in this study. The suggested method is simple in terms of hefty estimations as compared to standard ways because it avoids the well-known fixed point theory approach. It's also effective because it doesn't require any of the unnatural conditions that fixed point theory requires. Finally, we looked at a case study with simulation findings.

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

In this work, we calculate degenerate eigenstates of a coupled quartic oscillator with a high degree of chaoticity in a narrow energy window. For this purpose, we extend the range of applicability of the scar functions defined by us in F. Revuelta et al., Phys. Rev. E 102, 042210 (2020) to this more complicated case. Our method allows the reconstruction of individual eigenstates in terms of the shortest unstable periodic orbits of the system. As in the case of nondegenerate states, the basis size is of the same order of the number of computed eigenfunctions and depends on the ratio between the Heisenberg and the Ehrenfest times.

In this work, we calculate degenerate eigenstates of a coupled quartic oscillator with a high degree of chaoticity in a narrow energy window. For this purpose, we extend the range of applicability of the scar functions defined by us in F. Revuelta et al., Phys. Rev. E 102, 042210 (2020) to this more complicated case. Our method allows the reconstruction of individual eigenstates in terms of the shortest unstable periodic orbits of the system. As in the case of nondegenerate states, the basis size is of the same order of the number of computed eigenfunctions and depends on the ratio between the Heisenberg and the Ehrenfest times.

This paper proposes a new scheme for the solution of first order Riccati ordinary differential equations by means of the transcendental function of exponential type. The properties of the scheme were analyzed and investigated. Four numerical examples have been solved to test the performance of the scheme against exact solution and in terms of the absolute relative errors with different step sizes. The comparative analyses of the results were also presented.

This paper proposes a new scheme for the solution of first order Riccati ordinary differential equations by means of the transcendental function of exponential type. The properties of the scheme were analyzed and investigated. Four numerical examples have been solved to test the performance of the scheme against exact solution and in terms of the absolute relative errors with different step sizes. The comparative analyses of the results were also presented.

In this article, we consider a system of hyperbolic PDEs governed by the gravity wave model. From the application of symmetry analysis, we derive the group invariant exact solution for the governing system of equations. Further, through the solution in hand; we study the evolutionary behavior of weak discontinuity as well as characteristic shock. Finally, in order to highlight the physical significance, the interaction of weak discontinuity and characteristic shock is presented graphically.

In this article, we consider a system of hyperbolic PDEs governed by the gravity wave model. From the application of symmetry analysis, we derive the group invariant exact solution for the governing system of equations. Further, through the solution in hand; we study the evolutionary behavior of weak discontinuity as well as characteristic shock. Finally, in order to highlight the physical significance, the interaction of weak discontinuity and characteristic shock is presented graphically.

We study a coupled system of RL--type nonlinear fractional-order boundary value problems with a $p$-Laplacian operator in this paper. Using two Kernels, the considered coupled system can be transformed into an integral system. Due to the increased applicability of SFFPT to non-linear problems, sufficient conditions for the existence of positive solutions to the proposed problem are derived. Our technique for accomplishing these results is straightforward, but its application in the current context problem is new.

We study a coupled system of RL--type nonlinear fractional-order boundary value problems with a $p$-Laplacian operator in this paper. Using two Kernels, the considered coupled system can be transformed into an integral system. Due to the increased applicability of SFFPT to non-linear problems, sufficient conditions for the existence of positive solutions to the proposed problem are derived. Our technique for accomplishing these results is straightforward, but its application in the current context problem is new.

The present article deals with an eco-epidemiological model consisting of one prey and two predator population subjected to predator infection and predator harvesting. It has been considered two different types of functional response incorporating linear type refuge for susceptible predator and non-linear type refuge for infected predator. After formulating the model system, the positivity and boundedness of the solution, the persistence of the proposed system have been discussed. Along with the existence and stability of the biologically feasible equilibrium points, different types of bifurcation have been thoroughly investigated and in this regard, some suitable graphical representations are executed. Some numerical results are performed to support our analytical findings.

The present article deals with an eco-epidemiological model consisting of one prey and two predator population subjected to predator infection and predator harvesting. It has been considered two different types of functional response incorporating linear type refuge for susceptible predator and non-linear type refuge for infected predator. After formulating the model system, the positivity and boundedness of the solution, the persistence of the proposed system have been discussed. Along with the existence and stability of the biologically feasible equilibrium points, different types of bifurcation have been thoroughly investigated and in this regard, some suitable graphical representations are executed. Some numerical results are performed to support our analytical findings.

In this paper, we study the initial-boundary value problem for class of fractional $p-$Laplacian equation with logarithmic nonlinearity. By means of the Galerkin approximations, we prove the local and global existence of the weak solutions.We also establish finite time Blow up.

In this paper, we study the initial-boundary value problem for class of fractional $p-$Laplacian equation with logarithmic nonlinearity. By means of the Galerkin approximations, we prove the local and global existence of the weak solutions.We also establish finite time Blow up.

The approach of solving nonlinear models with numerical techniques is on the rise owing to the omnipresence of the models in several scientific fields. This paper developed an optimal variant of Halley's method without memory of order five for solving nonlinear equations $w(x)=0$. The technique is one-step with five function evaluations required in each iteration and has an efficiency index of $1.38$. The idea of basins of attraction to study the suggested technique's influence on the initial estimation is considered that reveals stable nature. This is also supported by various numerical examples that show how the proposed approach performs compared to other existing techniques. For examples considered, such as Vander Waals' equation and continuously stirred tank reactors, the proposed method without memory arrives at approximations to the roots with fewer iterations and better accuracy. Convergence analysis is also discussed to prove the fifth-order accuracy and complex dynamics is discussed via polynomiographs.

The approach of solving nonlinear models with numerical techniques is on the rise owing to the omnipresence of the models in several scientific fields. This paper developed an optimal variant of Halley's method without memory of order five for solving nonlinear equations $w(x)=0$. The technique is one-step with five function evaluations required in each iteration and has an efficiency index of $1.38$. The idea of basins of attraction to study the suggested technique's influence on the initial estimation is considered that reveals stable nature. This is also supported by various numerical examples that show how the proposed approach performs compared to other existing techniques. For examples considered, such as Vander Waals' equation and continuously stirred tank reactors, the proposed method without memory arrives at approximations to the roots with fewer iterations and better accuracy. Convergence analysis is also discussed to prove the fifth-order accuracy and complex dynamics is discussed via polynomiographs.

This study investigated the use of a $C^2$ rational cubic Ball function with four shape parameters to preserve the shape of positive, monotone, and convex data. It was found that by imposing some restrictions on two shape parameters the curve schemes will gain the shape of the data. However, the other two parameters are left free which gives an opportunity to refine the curve schemes as wanted to obtain a visually pleasing curve. The problem of visualization a constrained data is also considered, that when the data is located over a straight line and therefore the curve is required to locate on the same side of the line. Numerical examples and comparisons of the suggested method with other methods are mentioned.

This study investigated the use of a $C^2$ rational cubic Ball function with four shape parameters to preserve the shape of positive, monotone, and convex data. It was found that by imposing some restrictions on two shape parameters the curve schemes will gain the shape of the data. However, the other two parameters are left free which gives an opportunity to refine the curve schemes as wanted to obtain a visually pleasing curve. The problem of visualization a constrained data is also considered, that when the data is located over a straight line and therefore the curve is required to locate on the same side of the line. Numerical examples and comparisons of the suggested method with other methods are mentioned.

In this paper, two different types of synchronization between different chaotic systems with external disturbances in finite-time have been discussed. Further, chaotic and hyperchaotic systems have synchronized up to a desired transformation matrix. To numerically simulate generalized synchronization T chaotic system and a hyperchaotic system have been considered. In addition, modified generalized projective synchronization has been analyzed theoretically and numerically. Numerical results have shown through graphically and agreed with theoretical analysis.

In this paper, two different types of synchronization between different chaotic systems with external disturbances in finite-time have been discussed. Further, chaotic and hyperchaotic systems have synchronized up to a desired transformation matrix. To numerically simulate generalized synchronization T chaotic system and a hyperchaotic system have been considered. In addition, modified generalized projective synchronization has been analyzed theoretically and numerically. Numerical results have shown through graphically and agreed with theoretical analysis.

This research work proposes a novel method for controlling diabetes blood glucose levels. For the research of Type 1 Diabetes, we proposed a novel mathematical model. The homeostasis related with endocrinal logical regulation of glucose and glycogen levels in the human body by the hormones insulin and glucagon is attempted to be incorporated into a therapeutically feasible mathematical model. All plasma glucose concentrations, generalized insulin, and plasma insulin concentrations are taken into consideration by the model. Steady state analysis of the model is discussed. Local stability of the proposed model has been discussed using Routh-Hurwitz criteria. Global steadiness is also discussed. The numerical solution depicts the difficult condition faced by diabetes patients. MATLAB was used to carry out computer simulations for the analytical findings. As diabetics as very sensitive disease which is highly interrelated with various elements, in this perception we carried out computer simulations of various elements (attributes) in the segment of sensitivity analysis.

This research work proposes a novel method for controlling diabetes blood glucose levels. For the research of Type 1 Diabetes, we proposed a novel mathematical model. The homeostasis related with endocrinal logical regulation of glucose and glycogen levels in the human body by the hormones insulin and glucagon is attempted to be incorporated into a therapeutically feasible mathematical model. All plasma glucose concentrations, generalized insulin, and plasma insulin concentrations are taken into consideration by the model. Steady state analysis of the model is discussed. Local stability of the proposed model has been discussed using Routh-Hurwitz criteria. Global steadiness is also discussed. The numerical solution depicts the difficult condition faced by diabetes patients. MATLAB was used to carry out computer simulations for the analytical findings. As diabetics as very sensitive disease which is highly interrelated with various elements, in this perception we carried out computer simulations of various elements (attributes) in the segment of sensitivity analysis.

In this work, we derived the existence of mild solutions for fractional functional mixed integro-differential equations in Banach spaces. Standard fixed point techniques are used to obtained the results. Initially, we first formulate the definition of PC-mild solution and we prove the existence of solutions for the considered fractional system. Finally, we present an example to demonstrate the obtained theoretical results.

In this work, we derived the existence of mild solutions for fractional functional mixed integro-differential equations in Banach spaces. Standard fixed point techniques are used to obtained the results. Initially, we first formulate the definition of PC-mild solution and we prove the existence of solutions for the considered fractional system. Finally, we present an example to demonstrate the obtained theoretical results.

We consider coupling induced dissipation to study stochastic resonance (SR) phenomenon in a system of harmonic oscillators. Coupling through conjugate variables alludes dissipation in the coupled oscillatory systems by stabilising fixed points which are not stable in uncoupled state. We utilise this observation and investigate SR in coupled identical harmonic oscillators wherein dissipation is instigated by coupling forces. We extend the study to calculate second moment of mean field for harmonic oscillator (sixth order ode) analytically. The SR curves are also obtained numerically.

We consider coupling induced dissipation to study stochastic resonance (SR) phenomenon in a system of harmonic oscillators. Coupling through conjugate variables alludes dissipation in the coupled oscillatory systems by stabilising fixed points which are not stable in uncoupled state. We utilise this observation and investigate SR in coupled identical harmonic oscillators wherein dissipation is instigated by coupling forces. We extend the study to calculate second moment of mean field for harmonic oscillator (sixth order ode) analytically. The SR curves are also obtained numerically.