Vol. 14, No. 2 (2025): Regular Issue

The primary aim of this paper is to identify periodic solutions within an almost linear Volterra Integro-dynamic matrix Sylvester system operating on measure chains. Initially, we undertake a transformation of the Volterra Integro-dynamic matrix Sylvester system into the Kronecker Product Volterra Integro-dynamic System on measure chains through vectorization operations. Subsequent to this transformation, we proceed to establish the existence of periodic solutions for the Kronecker Product Volterra Integro-dynamic system on measure chains, by using Banach fixed point theorem. Importantly, our investigation extends to encompass periodic measure chains operating under both continuous and discrete conditions.

In this paper we will use new compact embedding and by Galerkin's approach we prove the existence of at least one solution to a p(x)-Kirchhoff problem with convection term and singular weights.

This article studied matrix projective synchronization (MPS) between chaotic systems with hyperbolic nonlinearity. The sufficient conditions for achieving matrix projective synchronization between coupled integer-order and fractional-order chaotic systems with hyperbolic nonlinearities have investigated. In case of matrix projective synchronization the controllers have designed to synchronize chaotic systems. In addition, numerical simulation is discussed to analyze theoretical study. It is also obtained that numerical results are agreed with theoretical results.

In this study, we prove the positive solutions to a fractional Volterra-Fredholm integro-differential equation existence and uniqueness. Along with integral boundary conditions, this equation uses Caputo-Hadamard fractional derivatives. Our method of proof makes use of the Schauder fixed point theorem, the Banach contraction principle, upper and lower solution notions, and these concepts. We present an example to demonstrate the utility of our theoretical conclusions.

In this study, we proposed a method for the pole optimization of the linear Muti Input Multi Output (MIMO)-Laguerre model using artificial bee colonies. The independent and orthonormal Laguerre basis is used to expand the system's inputs and outputs. The artificial bee colony (ABC) technique is used to model MIMO-Laguerre systems and the results are studied. Using this approach, the model parameters for the systems are generated and the algorithm's performance is compared with genetic algorithm and training functions. A numerical simulation to the CSTR Benchmark validates the optimization of Laguerre poles.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models.

In this study, we explore the controllability of dynamical systems by applying proportional fractional derivatives. The Grammian matrix technique is employed to establish both necessary and sufficient conditions that govern the controllability of linear fractional dynamical systems. Additionally, utilizing Schauder's fixed point theorem, we identify sufficient conditions for the controllability of nonlinear fractional dynamical systems. Numerous examples are provided to demonstrate and elucidate the theoretical findings.

In present research work, an iterative Shehu Adomian Decomposition Method is implemented to tackle the approximated and exact outcomes of the Fisher's Reaction-Diffusion equation. In present work, the Adomian polynomials are employed to fetch required terms in the process. The robustness and efficiency of the proposed technique are validated using the graphical matching of the outcomes. It can be assured that iterative Shehu ADM is one of the easy-to-implement techniques to tackle complex-natured PDEs. With the aid of the iterative Shehu ADM, a vast range of fractional PDEs can be solved as future research work.

In this paper, we introduce the optimal control problem for second order impulsive stochastic integro differential equations with infinite delay driven by fractional Brownian motion in Hilbert spaces. By using stochastic analysis theory and Krasnoselskii-Schaefer type fixed point theorem existence of mild solution is established. Next, conditions for the existence of optimal pair for these systems is also derived. Finally an example is given to illustrate theoretical results.

This paper aims to investigate the impacts of thermal diffusion and diffusion thermo on a steady, viscous, magnetohydrodynamic, incompressible, electrically conducting flow of an Oldroyd-B + nanofluid over a stretched sheet with mixed convection account taken. The study also considers the presence of chemical reactions, Schmidt number, Thermophoresis, Prandtl number, and Brownian motion effects. The current use of similarity variables broadens the scope of application for constitutive equations pertaining to mass, energy, and concentration. The finite element method is used to provide solutions for the given issue of governing equations. The Sherwood number, Nusselt number, and skin-friction coefficients are used to precisely measure the shear stress and the rates of heat and mass transfer at the boundary. Accurate numerical calculations may be accomplished using tables. In order to thoroughly analyze the dynamics of the issue, we conduct a detailed investigation of the tangible impacts of many factors. Afterwards, we use visual methods to emphasize and portray the resulting consequences. In addition, doing a comparison examination of current and previous outcomes provides a more comprehensive understanding of the memory effects.

To better understand how prey, predators, and super predators interact, a mathematical model has been developed. In the absence of a predator, it is thought that prey grows logistically. It is considered that a portion of prey may live outside the herd of prey and the remaining prey may live inside the herd of prey. It is also considered that predators and super predators may compete with one another within their species. Investigations have been done on the non-negativity and boundedness of the proposed model. The stability of the system is tested around each of the potential equilibrium points. Both theoretical and numerical studies of the Hopf bifurcation's existence conditions have been conducted. According to our study, if there is more prey outside the herd, it will be easier to hunt them, which could lead to an unstable ecology because of the increased predation pressure on the prey. It has been found that an increase in prey consumption rates can lead to ecosystem instability due to the herd of prey. It is observed that the increase of the environmental carrying capacity for prey i.e., if prey are living in a large area outside of the herd, then the hunting of prey may become easy for predators and it may make the ecosystem unstable. It is also evident that the ecology may have stabilized as a result of the super predator's increased saturation constant. A major consequence of the increase in predator conversion rates could be to disrupt the stability of the equilibrium of the model. It has been noted that the model might stabilize when intra-species competition rises.

In this paper, we aim to prove new results about the existence and uniqueness of solutions to fuzzy fractional Volterra-Fredholm integro-differential equations (FFV-FIDEs). These equations include fuzzy beginning conditions and generalized fuzzy Caputo-Hukuhara differentiability. The consecutive iteration approach and the Banach fixed point theorem are used in the proof. An example is provided to illustrate the main results.

In this article, we establish fairly general conditions 1) - 4) under which the Dirichlet problem for the parametrized elliptic partial differential equations involving p()-Laplacian has a weak solution in Sobolev spaces with variable exponents. The research employs variational methods and a mountain pass theorem in the variable exponent spaces. The existence of weak solutions to the Dirichlet boundary problem for the elliptic partial differential equation with a positive parameter $ \lambda$ is established in the variable exponent Sobolev space. The variable exponent Laplace equations play a prominent role in the modeling of diffusion processes with changing temperature and in fractional quantum mechanics. These results can be applied to image restoration problems.

This paper constructed a new 4D hyperchaotic system based on the generalized Hamiltonian forms. Through analysis of fundamental dynamical properties, including equilibrium points, stability, dissipative and conservative behaviors, bifurcation diagram, and Lyapunov exponents both numerically and analytically, this system exhibits a rich of dynamic features, encompassing hyperchaotic, chaotic, chaotic 2-tours, and periodic behaviors under certain parameters. Furthermore, the system is translated into an analog electronic circuit and simulated using an oscilloscope device, which achieved consistency between the MATLAB 2021 and Multisim 14.2 software simulations.

In this paper, we prove some new existence and uniqueness results of solutions for nonlinear fractional implicit integro-differential equations of Hadamard-Caputo type with fractional boundary conditions. The reasoning is inspired by diverse classical fixed point theory, such as the Schauder and Banach fixed point theorems. The theoretical findings are illustrated through an example.