Vol. 13, No. 3 (2024): Regular Issue

The main purpose of this paper is to study a class of non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. In our article we presented a coordinate-wise descent splitting method for non-stationary decomposable composite optimization problem and proved convergence of the problems involving the non-smooth set-valued functions. In our paper we gave a general iterative method and proved an existence result of solution for the non-stationary generalized mixed variational inequality problems.

The main purpose of this paper is to study a class of non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. In our article we presented a coordinate-wise descent splitting method for non-stationary decomposable composite optimization problem and proved convergence of the problems involving the non-smooth set-valued functions. In our paper we gave a general iterative method and proved an existence result of solution for the non-stationary generalized mixed variational inequality problems.

The stabilization of one-dimensional thermoelastic system of full von Kármán beam with a delayed linear frictional damping is considered, where the heat fux is given by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we prove that the system is exponentially stable. The idea here, is to generalize some previous existing results by considering a delayed problem.

The stabilization of one-dimensional thermoelastic system of full von Kármán beam with a delayed linear frictional damping is considered, where the heat fux is given by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we prove that the system is exponentially stable. The idea here, is to generalize some previous existing results by considering a delayed problem.

This paper investigates the brain tumor model describing the interactions between Glial cells, Sensitive Glioma cells, Resistant Glioma cells, and Neurons with Chemo-Virotherapy treatment. Chemo-Virotherapy has emerged as a promising novel cancer treatment to destroy glioma cells. The main aim is to kill tumor cells using virus-like Adenovirus and Herpes simplex virus-1 by virotherapy with Chemotherapy sessions. Stability Analysis is discussed under four categories: without any treatment, with chemotherapy treatment, with virotherapy treatment, and chemo-virotherapy treatment. Without any treatment, stability Analysis of the model shows that a tumor would grow to its maximum size. In the case of chemotherapy treatment, analysis of the model shows that the growth of resistant glioma cells increases at a quicker rate than healthy cells. Furthermore, virotherapy may not be able to remove glioma cells on its own, but if high viral potency viruses are used, they will reduce chemotherapy sessions. This analysis suggests that the combination therapy could lead to tremendous success in treating gliomas.

This paper investigates the brain tumor model describing the interactions between Glial cells, Sensitive Glioma cells, Resistant Glioma cells, and Neurons with Chemo-Virotherapy treatment. Chemo-Virotherapy has emerged as a promising novel cancer treatment to destroy glioma cells. The main aim is to kill tumor cells using virus-like Adenovirus and Herpes simplex virus-1 by virotherapy with Chemotherapy sessions. Stability Analysis is discussed under four categories: without any treatment, with chemotherapy treatment, with virotherapy treatment, and chemo-virotherapy treatment. Without any treatment, stability Analysis of the model shows that a tumor would grow to its maximum size. In the case of chemotherapy treatment, analysis of the model shows that the growth of resistant glioma cells increases at a quicker rate than healthy cells. Furthermore, virotherapy may not be able to remove glioma cells on its own, but if high viral potency viruses are used, they will reduce chemotherapy sessions. This analysis suggests that the combination therapy could lead to tremendous success in treating gliomas.

It is well-known to everyone that the system is very much disturbed by the past experience effect so past experiences should be incorporated into the system. For a rapidly changing market, the cost parameters of the inventory system are highly uncertain. Due to the above reasons, in this paper, we want to develop an EOQ model with a constant demand rate for non - deteriorating items where shortages are not allowed with Caputo fractional order derivative under a fuzzy environment. Here, we have used the concept "fractional order is an index of memory". Two types of memory indexes have been established. Memory effect has been observed by the step of long memory, short memory, and memoryless stages. The fractional order inventory model has been defuzzified using the graded mean integration method and signed distance method. Our numerical analysis clears us that profit is maximum for the presence of both memory indexes. In the long memory effect, inventory level changes roughly but this type of change happens, in reality, i.e., once increases then decrease again increases. From the graphical presentations, it can be suggested that there is a critical value of the ordering interval where long memory affected the total average cost and short memory affected total average cost becomes equal in both defuzzification techniques graded mean integration method, signed distance method.

It is well-known to everyone that the system is very much disturbed by the past experience effect so past experiences should be incorporated into the system. For a rapidly changing market, the cost parameters of the inventory system are highly uncertain. Due to the above reasons, in this paper, we want to develop an EOQ model with a constant demand rate for non - deteriorating items where shortages are not allowed with Caputo fractional order derivative under a fuzzy environment. Here, we have used the concept "fractional order is an index of memory". Two types of memory indexes have been established. Memory effect has been observed by the step of long memory, short memory, and memoryless stages. The fractional order inventory model has been defuzzified using the graded mean integration method and signed distance method. Our numerical analysis clears us that profit is maximum for the presence of both memory indexes. In the long memory effect, inventory level changes roughly but this type of change happens, in reality, i.e., once increases then decrease again increases. From the graphical presentations, it can be suggested that there is a critical value of the ordering interval where long memory affected the total average cost and short memory affected total average cost becomes equal in both defuzzification techniques graded mean integration method, signed distance method.

One of the calamities in the health sector during the recent years is COVID-19(Coronavirus Disease - 2019). The COVID-19 pandemic not only leads to a health crisis but also an economic and social crisis. To retrieve from this situation, it is essential to study the mathematical model of COVID-19. In this paper, a reaction-diffusion COVID-19 model, is considered. The aim of this article is to prove that the considered reaction-diffusion system with variable exponents has a unique weak solution. By regularizing the considered system and by using Faedo-Galerkin method, compactness result, and Gronwall lemma the main objective of the paper is obtained.

One of the calamities in the health sector during the recent years is COVID-19(Coronavirus Disease - 2019). The COVID-19 pandemic not only leads to a health crisis but also an economic and social crisis. To retrieve from this situation, it is essential to study the mathematical model of COVID-19. In this paper, a reaction-diffusion COVID-19 model, is considered. The aim of this article is to prove that the considered reaction-diffusion system with variable exponents has a unique weak solution. By regularizing the considered system and by using Faedo-Galerkin method, compactness result, and Gronwall lemma the main objective of the paper is obtained.

This paper investigates the heat and mass transfer of an unsteady, MHD incompressible water-based nanofluids (Cu and TiO2) flow over a stretching sheet in a transverse magnetic field with thermal radiation Soret effects in the presence of Heat source and chemical reaction. The governing differential equations are transformed into a set of non-linear ordinary differential equations and solved using a regular perturbation technique with appropriate boundary conditions for various physical parameters. The effects of different physical parameters on the dimensionless velocity, temperature, and concentration profiles are depicted graphically and analyzed in detail. Finally, numerical values of the physical quantities, such as the local skin-friction coefficient, the Nusselt number and the Sherwood number, are presented in tabular form. It is concluded that the resultant velocity reduces with increasing Jeffrey parameter and magnetic field parameter, Results describe that the velocity and temperature diminish with enhancing the thermal radiation. Both velocity and concentration are enhanced with increases of soret parameter. Also it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameter. It is because chemical molecular diffusivity reduces for higher values of Chemical reaction parameter. Also, water-based TiO2 nanofluids possess higher velocity than water-based Cu nanofluids. Comparisons with previously published work performed and the results are found to be in the excellent agreement. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

This paper investigates the heat and mass transfer of an unsteady, MHD incompressible water-based nanofluids (Cu and TiO2) flow over a stretching sheet in a transverse magnetic field with thermal radiation Soret effects in the presence of Heat source and chemical reaction. The governing differential equations are transformed into a set of non-linear ordinary differential equations and solved using a regular perturbation technique with appropriate boundary conditions for various physical parameters. The effects of different physical parameters on the dimensionless velocity, temperature, and concentration profiles are depicted graphically and analyzed in detail. Finally, numerical values of the physical quantities, such as the local skin-friction coefficient, the Nusselt number and the Sherwood number, are presented in tabular form. It is concluded that the resultant velocity reduces with increasing Jeffrey parameter and magnetic field parameter, Results describe that the velocity and temperature diminish with enhancing the thermal radiation. Both velocity and concentration are enhanced with increases of soret parameter. Also it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameter. It is because chemical molecular diffusivity reduces for higher values of Chemical reaction parameter. Also, water-based TiO2 nanofluids possess higher velocity than water-based Cu nanofluids. Comparisons with previously published work performed and the results are found to be in the excellent agreement. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

In this paper we have considered a predator-prey system under harvesting. The prey population obey the law of logistic growth. The predator functional response to prey density is taken in such a manner that when prey population increase the predator's functional response tends to a constant value. The predator population are under competition among themselves. The existence of the solution of the nonlinear system are carried out. The steady states and the stability of the system are analyzed. We have tested the stability of the models system at the equilibrium points by using variational method. The existence of bionomic equilibrium has been carried out. The Pontryagin's maximum principle has been used for the analysis of the optimal harvesting policy of the model system.

In this paper we have considered a predator-prey system under harvesting. The prey population obey the law of logistic growth. The predator functional response to prey density is taken in such a manner that when prey population increase the predator's functional response tends to a constant value. The predator population are under competition among themselves. The existence of the solution of the nonlinear system are carried out. The steady states and the stability of the system are analyzed. We have tested the stability of the models system at the equilibrium points by using variational method. The existence of bionomic equilibrium has been carried out. The Pontryagin's maximum principle has been used for the analysis of the optimal harvesting policy of the model system.

We study a discrete-time dynamical system of wild mosquito population with parameters: $\beta$ - the birth rate of adults; $\alpha$ - maximum emergence rate; $\mu>0$ - the death rate of adults; $\gamma$ - Allee effects. We prove that if $\gamma\geq\frac{\alpha(\beta-\mu)}{\mu^2}$ then the mosquito population dies and if $\gamma<\frac{\alpha(\beta-\mu)}{\mu^2}$ holds then extinction or survival of the mosquito population depends on their initial state.

We study a discrete-time dynamical system of wild mosquito population with parameters: $\beta$ - the birth rate of adults; $\alpha$ - maximum emergence rate; $\mu>0$ - the death rate of adults; $\gamma$ - Allee effects. We prove that if $\gamma\geq\frac{\alpha(\beta-\mu)}{\mu^2}$ then the mosquito population dies and if $\gamma<\frac{\alpha(\beta-\mu)}{\mu^2}$ holds then extinction or survival of the mosquito population depends on their initial state.

The COVID-19 pandemic has troubled both medicinal and scientific personnel for more than two years. This epidemic has proven resilient to medical and social measures undertaken worldwide. Modeling a pandemic of this size is an arduous task, partly because of the virus' mutability and partly due to the diverse and complex ways that each government is trying to reduce the effects of the pandemic, by using different measures with a varying degree of success. In this work, we will try to design an adaptable dynamical system, which can be adjusted to make predictions for different populations and different measures to fight the pandemic. Additionally, we will present a novel idea for examining whether an epidemiological system, i.e., the epidemic will end or not in-dependently of the system's internal characteristics.

The COVID-19 pandemic has troubled both medicinal and scientific personnel for more than two years. This epidemic has proven resilient to medical and social measures undertaken worldwide. Modeling a pandemic of this size is an arduous task, partly because of the virus' mutability and partly due to the diverse and complex ways that each government is trying to reduce the effects of the pandemic, by using different measures with a varying degree of success. In this work, we will try to design an adaptable dynamical system, which can be adjusted to make predictions for different populations and different measures to fight the pandemic. Additionally, we will present a novel idea for examining whether an epidemiological system, i.e., the epidemic will end or not in-dependently of the system's internal characteristics.

A physical model is developed to investigate the combined effects of internal heat source, mass flow and viscous dissipation on the Hadley-Prats flow in an infinite parallel horizontal porous layer with the inclined temperature gradient. Following non-dimensionalization of the model, a linear instability analysis is conducted and the basic steady state solution is derived. Transverse or longitudinal roll disturbances are examined. The eigenvalue problem is solved using Runge-Kutta and shooting methods to determine the eigenvalues as the vertical values of the thermal Rayleigh number $R_z$ for both cases of disturbances i.e. longitudinal and transverse rolls. The critical wave number and critical vertical thermal Rayleigh number $R_z$ are identified for different thermo physical parameters. The conceptual study is constructed to comprehend the consequence of the viscous dissipation of the mono-diffusive instability analysis of Hadley-Prats flow thermal convection in the fluid saturated infinite horizontal porous layer. The simulations show that increased internal heat generation causes efficient destabilisation in all areas, since it raises the overall temperature of the system. Higher values of horizontal Rayleigh number $R_x$, and with viscous dissipation generally result in a decrease in critical vertical Rayleigh number and therefore flow destabilization in the porous medium. Physical interpretation of the numerical solutions relating to the linear instability analysis is presented.

A physical model is developed to investigate the combined effects of internal heat source, mass flow and viscous dissipation on the Hadley-Prats flow in an infinite parallel horizontal porous layer with the inclined temperature gradient. Following non-dimensionalization of the model, a linear instability analysis is conducted and the basic steady state solution is derived. Transverse or longitudinal roll disturbances are examined. The eigenvalue problem is solved using Runge-Kutta and shooting methods to determine the eigenvalues as the vertical values of the thermal Rayleigh number $R_z$ for both cases of disturbances i.e. longitudinal and transverse rolls. The critical wave number and critical vertical thermal Rayleigh number $R_z$ are identified for different thermo physical parameters. The conceptual study is constructed to comprehend the consequence of the viscous dissipation of the mono-diffusive instability analysis of Hadley-Prats flow thermal convection in the fluid saturated infinite horizontal porous layer. The simulations show that increased internal heat generation causes efficient destabilisation in all areas, since it raises the overall temperature of the system. Higher values of horizontal Rayleigh number $R_x$, and with viscous dissipation generally result in a decrease in critical vertical Rayleigh number and therefore flow destabilization in the porous medium. Physical interpretation of the numerical solutions relating to the linear instability analysis is presented.

In this manuscript, we are mainly investigating the existence of the mild solution for the Hilfer fractional Volterra-Fredholm differential systems via almost sectorial operator. The nonlinear alternative Leray-Schauder fixed point technique for multivalued maps is applied to the fractional calculus concept to demonstrate the conclusions. Finally, an application is provided to demonstrate how the major results might be applied.

In this manuscript, we are mainly investigating the existence of the mild solution for the Hilfer fractional Volterra-Fredholm differential systems via almost sectorial operator. The nonlinear alternative Leray-Schauder fixed point technique for multivalued maps is applied to the fractional calculus concept to demonstrate the conclusions. Finally, an application is provided to demonstrate how the major results might be applied.

The goal of this research is to understand the influences of Joule heating and aligned magnetic field with fluid flows on an exponential shrinking sheet. Relevant similarity transformations are used to extract ordinary differential equations (ODE's) from the associated flow governing partial differential equations (PDE's). The set of resulting ODEs is solved by a shooting algorithm, which utilizes the Runge-Kutta and Newton-Raphson techniques. The impact of magnetic and Joule heating parameters on the fluid velocity and fluid temperature profiles, as well as the skin friction coefficient and heat transfer rate, are investigated. As a result, the multiple solutions are appearing for each combination and hence, the stability solutions are extracted using temporal stability analysis. In addition, the streamline patterns are provided graphically along with the eigenvalue behavior for each of these solutions. Moreover, the flow separation is identified in the shrinking region. This type of research is extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines and high-performance automatic parts) and medicine.

The goal of this research is to understand the influences of Joule heating and aligned magnetic field with fluid flows on an exponential shrinking sheet. Relevant similarity transformations are used to extract ordinary differential equations (ODE's) from the associated flow governing partial differential equations (PDE's). The set of resulting ODEs is solved by a shooting algorithm, which utilizes the Runge-Kutta and Newton-Raphson techniques. The impact of magnetic and Joule heating parameters on the fluid velocity and fluid temperature profiles, as well as the skin friction coefficient and heat transfer rate, are investigated. As a result, the multiple solutions are appearing for each combination and hence, the stability solutions are extracted using temporal stability analysis. In addition, the streamline patterns are provided graphically along with the eigenvalue behavior for each of these solutions. Moreover, the flow separation is identified in the shrinking region. This type of research is extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines and high-performance automatic parts) and medicine.

The influence of first-order chemical reaction and rotation on the onset of convection in a sparsely packed porous layer heated continuously from the bottom is explored numerically using linear stability analysis. The boundaries of fluid are considered as either free or rigid. Eigenvalue problem for three different boundaries of the fluid are solved using bvp4c in MATLAB R2022a. Effects of Damköhler number, Lewis number, solutal Rayleigh number, Taylor number and Darcy number are analyzed. The critical Rayleigh number $(Ra_c)$ and wavenumber $(a_c)$ are calculated and shown in tables for different boundary conditions. It is found that increasing the Taylor number inhibits the onset of convection. On the other hand Damköhler number is observed to have destabilizing effect on the system. It is found that critical wave number does not depend on Lewis number, solutal Rayleigh number and Damköhler number hence it has no impact on the size of convection cells. Critical wave number is an increasing function of Taylor number, so the size of convection cells decreases. The effect of Darcy number is to increase the size of convection cells because critical wave number decreases with Darcy number.

The influence of first-order chemical reaction and rotation on the onset of convection in a sparsely packed porous layer heated continuously from the bottom is explored numerically using linear stability analysis. The boundaries of fluid are considered as either free or rigid. Eigenvalue problem for three different boundaries of the fluid are solved using bvp4c in MATLAB R2022a. Effects of Damköhler number, Lewis number, solutal Rayleigh number, Taylor number and Darcy number are analyzed. The critical Rayleigh number $(Ra_c)$ and wavenumber $(a_c)$ are calculated and shown in tables for different boundary conditions. It is found that increasing the Taylor number inhibits the onset of convection. On the other hand Damköhler number is observed to have destabilizing effect on the system. It is found that critical wave number does not depend on Lewis number, solutal Rayleigh number and Damköhler number hence it has no impact on the size of convection cells. Critical wave number is an increasing function of Taylor number, so the size of convection cells decreases. The effect of Darcy number is to increase the size of convection cells because critical wave number decreases with Darcy number.

The main goal of this paper is to study the existence and uniqueness of periodic solutions for some class of nonlinear fractional coupled systems with $\psi-$Hilfer derivative. The proofs are based upon the coincidence degree theory of Mawhin with several types of conditions. To show the efficiency of the stated result, illustrative examples will be given.

The main goal of this paper is to study the existence and uniqueness of periodic solutions for some class of nonlinear fractional coupled systems with $\psi-$Hilfer derivative. The proofs are based upon the coincidence degree theory of Mawhin with several types of conditions. To show the efficiency of the stated result, illustrative examples will be given.