An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

Certain saigo type fractional integral inequalities and their q-analogues

2023-01-24T00:10:00+03:00

The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

2023-01-24T00:10:03+03:00

In this work, we introduce a simple method for investigating the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov's indirect method. This method is constructed based on the classical Lyapunov's indirect method and the idea proposed by Ghaffari and Lasemi in a recent work. The new method can be applicable even when equilibia of dynamical systems are non-hyperbolic. Hence, in many cases, the classical Lyapunov's indirect method fails but the new one can be used simply. In addition, by combining the new stability method with the Mickens' methodology, we formulate some nonstandard finite difference (NSFD) methods which are able to preserve the asymptotic stability of some classes of differential equation models even when they have non-hyperbolic equilibrium points. As an important consequence, some well-known results on stability-preserving NSFD schemes for autonomous dynamical systems are improved and extended. Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.

Observer design for a class of irreversible port Hamiltonian systems

2023-01-24T00:10:05+03:00

In this paper we address the state estimation problem of a particular class of irreversible port Hamiltonian systems (IPHS), which are assumed to be partially observed. Our main contribution consists to design an observer such that the augmented system (plant + observer) is strictly passive. Under some additional assumptions, a Lyapunov function is constructed to ensure the stability of the coupled system. Finally, the proposed methodology is applied to the gas piston system model. Some simulation results are also presented.

The effect of marketing and R&D expenditures on firm profitability and stock return: Evidence from BIST

2023-01-24T00:09:58+03:00

This study aims to determine the effects of R&D and marketing expenditures of companies that force marketing and finance to act together on stock return, return on assets, and return on equity. To this end, the quarterly frequency data of nine companies that were continuously traded in the BIST Technology Index between March 2009 and December 2020 were examined with panel-data analysis. In line with the purpose of the research, analyzes were carried out in three different models. First of all, we determined which tests should be performed on the models based on the cross-sectional dependence, homogeneity/heterogeneity, and panel unit root test results obtained for the established models. The results of panel least squares test carried out to determine the effect of R&D and marketing expenditures on stock return showed that the effect of R&D expenditures on stock return was not statistically significant while marketing expenditures had a positive and significant effect on stock return. Analyzes should be continued with cointegration tests according to the characteristics of the two models established to determine the effect of R&D and marketing expenditures on return on assets and return on equity. The results implied a positive and significant relationship between R&D expenditures and return on both assets and equity. While no statistically significant relationship was found between marketing expenditures and return on assets, there was a positive and significant relationship between marketing expenditures and return on equity.

Novel approach for nonlinear time-fractional Sharma-Tasso-Olever equation using Elzaki transform

2023-01-26T03:59:26+03:00

In this article, we demonstrated the study of the time-fractional nonlinear Sharma-Tasso-Olever (STO) equation with different initial conditions. The novel technique, which is the mixture of the q-homotopy analysis method and the new integral transform known as Elzaki transform called, q-homotopy analysis Elzaki transform method (q-HAETM) implemented to find the adequate approximated solution of the considered problems. The wave solutions of the STO equation play a vital role in the nonlinear wave model for coastal and harbor designs. The demonstration of the considered scheme is done by carrying out some examples of time-fractional STO equations with different initial approximations. q-HAETM offers us to modulate the range of convergence of the series solution using , called the auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations, the effectiveness and reliability of the considered technique are validated. The implementation of the new integral transform called the Elzaki transform along with the reliable analytical technique called the q-homotopy analysis method to examine the time-fractional nonlinear STO equation displays the novelty of the presented work. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives

2023-01-28T06:35:47+03:00

The article objectifies the approximate controllability of fractional nonlinear differential equations having Riemann-Liouville derivatives. First, the existence of solutions is deduced through fixed point approach and then approximate controllability is proved using Cauchy convergence through iterative and approximate techniques. The theory of semigroup together with probability density function has been utilized to reach the desired conclusions.

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

2023-01-28T06:35:33+03:00

This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.

The processes with fractional order delay and PI controller design using particle swarm optimization

2023-01-27T06:35:19+03:00

In this study, the stability analysis of systems with fractional order delay is presented. Besides, PI controller design using particle swarm optimization (PSO) technique for such systems is also presented. The PSO algorithm is used to obtain the controller parameters within the stability region. As it is known that it is not possible to investigate the stability of systems with fractional order delay using analytical methods such as the Routh-Hurwitz criterion. Furthermore, stability analysis of such systems is quite difficult. In this study, for stability testing of such systems, an approximation method previously introduced in the literature by the corresponding author is used. In addition, the unit step responses have been examined to evaluate the systems' performances. It should be noted that examining unit step responses of systems having fractional-order delay is not possible due to the absence of analytical methods. One of the aims of this study is to overcome this deficiency by using the proposed approximation method. Besides, a solution to the question of which controller parameter values should be selected in the stability region, which provides the calculation of all stabilizing PI controllers, is proposed using the PSO algorithm.

Stability tests and solution estimates for non-linear differential equations

2023-01-29T22:23:17+03:00

This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovski? functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.

Analysing the market for digital payments in India using the predator-prey mode

2023-01-29T23:18:56+03:00

Technology has revolutionized the way transactions are carried out in economies across the world. India too has witnessed the introduction of numerous modes of electronic payment in the past couple of decades, including e-banking services, National Electronic Fund Transfer (NEFT), Real Time Gross Settlement (RTGS) and most recently the Unified Payments Interface (UPI). While other payment mechanisms have witnessed a gradual and consistent increase in the volume of transactions, UPI has witnessed an exponential increase in usage and is almost on par with pre-existing technologies in the volume of transactions. This study aims to employ a modified Lotka-Volterra (LV) equations (also known as the Predator-Prey Model) to study the competition among different payment mechanisms. The market share of each platform is estimated using the LV equations and combined with the estimates of the total market size obtained using the Auto-Regressive Integrated Moving Average (ARIMA) technique. The result of the model predicts that UPI will eventually overtake the conventional digital payment mechanism in terms of market share as well as volume. Thus, the model indicates a scenario where both payment mechanisms would coexist with UPI being the dominant (or more preferred) mode of payment.

The null boundary controllability for the Mullins equation with periodic boundary conditions

2023-01-29T23:18:58+03:00

In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class.

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

2023-01-29T23:42:17+03:00

This article aims to examine M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation (FE), which is a generalization of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The fractional (4+1)$-dimensional Fokas equation with the M-truncated derivatives is also studied first time in this study. The generalized projective Riccati equations method (GPREM) is successfully implemented. In the application of the presented method, a suitable fractional wave transformation is chosen to convert the proposed model into a nonlinear ordinary differential equation. Then, a linear equation system is acquired utilizing the GPREM, the system is solved, and the suitable solution sets are obtained. Dark and singular soliton solutions are successfully derived. Under the selection of appropriate values of the parameters, 2D, 3D, and contour plots are also displayed for some solutions.

A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

2023-02-01T06:46:02+03:00

The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper. We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system. The application of well-known fixed point theorem methodologies is avoided in this paper. Finally, a fractional heat equation is discussed as an example.