Kanokwan Sitthithakerngkiet

• PhD
• Lecturer at King Mongkut's University of Technology North Bangkok, Bangkok, Thailand

The paper introduces two new methods, termed relaxed dual inertial extragradient methods, which incorporate a self-adaptive step size strategy. These methods are developed to approximate solutions to pseudomonotone variational inequality problems and fixed-point problems associated with \(\chi \)-demicontractive mappings in real Hilbert spaces. The...

This study presents a fresh perspective on the existence, uniqueness, and stability of solutions for initial value problems involving variable-order differential equations with finite delay. Departing from conventional techniques that utilize generalized intervals and piecewise constant functions, we introduce a novel fractional operator tailored f...

This paper introduces a new algorithmic framework for solving pseudomonotone equilibrium problems and demicontractive fixed‐point problems. Unlike conventional methods that incorporate a single inertial step, our approach employs dual inertia to accelerate convergence while preserving stability. The proposed method combines the viscosity approximat...

This paper presents an enhanced algorithm designed to solve variational inequality problems that involve a pseudomonotone and Lipschitz continuous operator in real Hilbert spaces. The method integrates a dual inertial extrapolation step, a relaxation step, and the subgradient extragradient technique, resulting in faster convergence than existing in...

This paper investigates the flow of a second‐grade viscoelastic fluid with dust particles under hydromagnetic effects between vertical plates. This study investigates the effects of the left plate's oscillations, which induce fluid motion, on heat and mass transfer, and particle temperature. The study also considers the variable temperature and con...

Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, ‘PRP,’ ‘HS,’ and ‘DL,’ do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property ind...

In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed...

Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which...

In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for increased acceleration. Moreover, we d...

The main objective is to apply the concept of newly developed idea of the fractional‐order derivative of the Rabotnov fractional–exponential function in fluid dynamics. In this article, a newly developed idea of the fractional‐order derivative of the Rabotnov fractional–exponential function and the nonsingular kernel has been applied to study visco...

The goal of this work is to study a multi-term boundary value problem (BVP) for fractional differential equations in the variable exponent Lebesgue space (Lp(·)). Both the existence, uniqueness, and the stability in the sense of Ulam–Hyers are established. Our results are obtained using two fixed-point theorems, then illustrating the results with a...

In this paper, we establish a modified proximal point algorithm for solving the common problem between convex constrained minimization and modified variational inclusion problems. The proposed algorithm base on the proximal point algorithm in [19] and the method of Khuangsatung and Kangtunyakarn in [21] by using suitable conditions in Hilbert space...

Electro-osmotic flow via a microchannel has numerous uses in the contemporary world, including in the biochemical and pharmaceutical industries. This research explores the electroosmotic flow of Casson-type nanofluid with Sodium Alginate nanoparticles through a vertically tilted microchannel. In addition, the transverse magnetic field is also consi...

The steady‐state laminar nonisothermal, incompressible viscoelastic fluid flows with the Jeffrey model between two counterrotating (same direction) rolls are studied analytically. The Jeffrey model is reduced to the Newtonian model after some appropriate modifications. The new dimensionless governing equations are acquired through suitable nondimen...

Recent developments in split equilibrium problems (SEPs) have found practical applications in convex optimization problems, information theory, and signal processing. In this paper, we present three novel algorithms with no prior knowledge of the operator norm of a bounded linear operator to approximated solutions for SEPs. Strong convergence resul...

The outcome of Newtonian heating on the viscoelastic fluid plays a vital role in daily life applications such as conjugate heat transfer around fins, heat exchanger, solar radiation, petroleum industry, etc. Also, rotation of viscoelastic fluid has various importance in product-making industries and engineering. Viscoelastic dusty fluids and Newton...

To control the complicated rheological behavior of fluid models, several mathematical approaches have been established. Empirical, statistical, iterative, and analytical approaches are used to study such mathematical models. Consequently, this paper provides an analytical analysis and assessment of the Laplace, and Sumudu transforms for the unstead...

Usually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures. In this article, a very accurate and prominent m...

In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately. The residual power series method (RPSM) is used for the solution analysis of fractional partial differential equations (FPDEs), which has di...

The thermal distribution in a convective-radiative concave porous fin appended to an inclined surface has been examined in this research. The equation governing the temperature and heat variation in fin with internal heat generation is transformed using non-dimensional variables, and the resulting partial differential equation (PDE) is tackled usin...

Cancer is clearly a major cause of disease and fatality around the world, yet little is known about how it starts and spreads. In this study, a model in mathematical form of breast cancer guided by a system of (ODE’S) ordinary differential equations is studied in depth to examine the thermal effects of various shape nanoparticles on breast cancer h...

The solutions to fractional differentials equations are very difficult to investigate. In particular, the solutions of fractional partial differential equations are challenging tasks for mathematicians. In the present article, an extension to this idea is presented to obtain the solutions of non-linear fractional Korteweg–de Vries equations. The so...

The main goal of this inspection is to explore the heat and mass transport phenomena of a three-dimensional MHD flow of ternary hybrid nanoliquid through a porous media toward a stretching surface. Because nowadays the low thermal conductivity is the key problem for scientist and researchers in the transmission of heat processes. Therefore, in orde...

The dynamic of fluids and coolants in automobiles are achieved by enhancement in heat energy using ternary hybrid nanostructures. Ternary hybrid nanomaterial is obtained by suspension of three types of nanofluid (aluminum oxide, silicon dioxide and titanium dioxide) in base fluid (EG). Prime investigation is to address comparison study in thermal e...

The mechanism of thermal transport can be enhanced by mixing the nanoparticles in the base liquid. This research discusses the utilization of nanoparticles (tri-hybrid) mixture into Carreau–Yasuda material. The flow is assumed to be produced due to the stretching of vertical heated surface. The phenomena of thermal transport are modeled by consider...

In this article, a new modification of the Adomian decomposition method is performed for the solution fractional order convection–diffusion equation with variable coefficient and initial–boundary conditions. The solutions of the suggested problems are calculated for both fractional and integer orders of the problems. The series of solutions of the...

In this paper, we compute a common solution of the fixed point problem (FPP) and the generalized split common null point problem (GSCNPP) via the inertial hybrid shrinking approximants in Hilbert spaces. We show that the approximants can be easily adapted to various extensively analyzed theoretical problems in this framework. Finally, we furnish a...

The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).

This comparative study of fractional nonlinear fractional Burger’s equations and their systems has been done using two efficient analytical techniques. The generalized schemes of the proposed techniques for the suggested problems are obtained in a very sophisticated manner. The numerical examples of Burger’s equations and their systems have been so...

This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of $ \eta $-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation techniqu...

In this research article the residual power series method is implemented for the solution of the Navier-stokes equations with two and three dimensions having the initial conditions. Caputo operator is used for the fractional derivative. The formulation is made in general form and then applied to the specific problems to check the validity of the su...

In the present work, an Elzaki transformation is combined with a decomposition technique for the solutions of fractional dynamical systems. The targeted problems are related to the systems of fractional partial differential equations. Fractional differential equations are useful for more accurate modeling of various phenomena. The Elzaki transform...

Clean energy potential can be used on a large scale in order to achieve cost competitiveness and market effectiveness. This paper offers sufficient information to choose renewable technology for improving the living conditions of the local community while meeting energy requirements by employing the notion of q-rung orthopair fuzzy numbers (q-ROFNs...

In the current note, we broaden the utilization of a new and efficient analytical computational scheme, approximate analytical method for obtaining the solutions of fractional-order Fokker-Planck equations. The approximate solution is obtained by decomposition technique along with the property of Riemann-Liouuille fractional partial integral operat...

The purpose of this work is to construct iterative methods for solving a split minimization problem using a self-adaptive step size, conjugate gradient direction, and inertia technique. We introduce and prove a strong convergence theorem in the framework of Hilbert spaces. We then demonstrate numerically how the extrapolation factor (θn) in the ine...

In this work, an evolving definition of the fractal-fractional operator with exponential kernel was employed to examine Casson fluid flow with the electro-osmotic phenomenon. Electrically conducted Casson fluid flow with the effect of the electro-osmotic phenomenon has been assumed in a vertical microchannel. With the help of relative constitutive...

Smart mobile devices are being widely used to identify and track human behaviors in simple and complex daily activities. The evolution of wearable sensing technologies pertaining to wellness, living surveillance, and fitness tracking is based on the accurate analysis of people’s behavior from the data acquired through different sensors embedded in...

A new technique of the Adomian decomposition method is developed and applied in this research article to solve two-term diffusion wave and fractional telegraph equations with initial-boundary conditions. The proposed technique is used to solve problems of both fractional and integer orders of the telegraph equations. The fractional-order solutions...

The goal of this study was to show how a modified variational inclusion problem can be solved based on Tseng’s method. In this study, we propose a modified Tseng’s method and increase the reliability of the proposed method. This method is to modify the relaxed inertial Tseng’s method by using certain conditions and the parallel technique. We also p...

This article proposes a strong convergence C Q relaxed iterative method with alternated inertial extrapolation step in a real Hilbert space. The propose method converges strongly under some suitable and easy to verify assumptions. Moreover, the proposed method does not require the prior knowledge of the operator norm or estimate of the matrix norm....

In recent times, the study of diathermal oils is an area of interest for multiple researchers because of their numerous pivotal applications in industrial and engineering operations. The core aim of this work is the formulation of a fractional model to anticipate improvement in thermal and flow characteristics of a particular kind of diathermal oil...

In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide (MoS2) nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid...

Variational inclusion is an important general problem consisting of many useful problems like variational inequality, minimization problem and nonlinear monotone equations. In this article, a new scheme for solving variational inclusion problem is proposed and the scheme uses inertial and relaxation techniques. Moreover, the scheme is self adaptive...

In this paper, we propose a new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems without pseudomonotonicity of the bifunction f in a real Hilbert space. When setting the solution of dual equilibrium problem is nonempty, we obtain a strong convergence theorem which is generated by the iterative...

In this paper, a new derivative-free approach for solving nonlinear monotone system of equations with convex constraints is proposed. The search direction of the proposed algorithm is derived based on the modified scaled Davidon-Fletcher-Powell (DFP) updating formula in such a way that it is sufficiently descent. Under some mild assumptions, the se...

In this paper, a new self-adaptive step size algorithm to approximate the solution of the split minimization problem and the fixed point problem of nonexpansive mappings was constructed, which combined the proximal algorithm and a modified Mann’s iterative method with the inertial extrapolation. The strong convergence theorem was provided in the fr...

Many problems in engineering and social sciences can be transformed into system of nonlinear equations. As a result, a lot of methods have been proposed for solving the system. Some of the classical methods include Newton and Quasi Newton methods which have rapid convergence from good initial points but unable to deal with large scale problems due...

The Spectral conjugate gradient (SCG) methods are among the efficient variants of CG algorithms which are obtained by combining the spectral gradient parameter and CG parameter. The success of SCG methods relies on effective choices of the step-size αk and the search direction dk. This paper presents an SCG method for unconstrained optimization mod...

In this paper, we study a monotone inclusion problem in the framework of Hilbert spaces. (1) We introduce a new modified Tseng’s method that combines inertial and viscosity techniques. Our aim is to obtain an algorithm with better performance that can be applied to a broader class of mappings. (2) We prove a strong convergence theorem to approximat...

A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-orde...

The prime aim of this article is the construction of a fractional model to enhance the heat transfer rate for magnetohydrodynamic (MHD) convectional transport of ferrofluid by applying the time-fractional concept of Caputo-Fabrizio derivative on Brinkman type fluid model. Kerosene oil and water are considered to serve as carrier fluids for iron oxi...

Abstract In this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was c...

This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By emplo...

In this paper, we study an iterative method for solving the multiple-set split feasibilityproblem: find a point in the intersection of a finite family of closed convex sets in one space suchthat its image under a linear transformation belongs to the intersection of another finite family ofclosed convex sets in the image space. In our result, we obt...

In this paper, we study and consider the positive solution of fractional differential equation with nonlocal multi-point conditions of the from: RL D q 0 + u(t) + g(t)f (t, u(t)) = 0, t ∈ (0, 1) u (k) (0) = 0, u(1) = m i=1 β i RL D p i 0 + u(η i) where n − 1 < q < n, n ≥ 2, n − 1 < p i < n, q > p i m, n ∈ N, k = 0, 1, · · · , n − 2, 0 < η 1 < η 2 <...

Abstract In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts...

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition,...

One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations. In this research article, we present a modification of the Fletcher–Reeves (FR) conjugate gradient...

In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward–backward splitting algorithm. In addition, we have discussed the application of this algorithm.

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): cD0+qu(t)=f(t,u(t)),t∈[0,T], u(k)(0)=ξk,u(T)=∑i=1mβiRLI0+piu(ηi), where n−1<q<n,n≥2,m,n∈N, ξk,βi∈R, k=0,1,…,n−2, i=1,2,…,m, and cD0+q is the Caputo fractional derivatives, f:[0,T]×C([0,T],E)→E, where E is...

Based on the very recent work by Shehu and Agbebaku in Comput. Appl. Math. 2017, we introduce an extension of their iterative algorithm by combining it with inertial extrapolation for solving split inclusion problems and fixed point problems. Under suitable conditions, we prove that the proposed algorithm converges strongly to common elements of th...

This paper is devoted to solving the following accretive variational inequality for finding x∗∈Fix(T) such that ⟨Ax∗,j(x-x∗)⟩≥0,∀x∈Fix(T),where j(x-x∗)∈J(x-x∗), A is an accretive operator and Fix(T) is the set of fixed points of pseudo-contraction T. For this purpose, we construct an implicit algorithm and prove its convergence hierarchical to the...

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontr...

The main purpose in this paper is to define the modification form of random α-admissible and random α-ψ-contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to...

In this work, we introduced new notions of a new contraction named S-weakly contraction; after that, we obtained the p-common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak Pp-property and proved the uniqueness of these points. Also, we presented some examples to prove the val...

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of split variational inclusion problem in the framework Hilbert spaces. Strong convergence theorem of the sequences generated by the purpose iterative scheme i...

In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete b-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatte...

We modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is established and the illustrative numerical example is pr...

In this paper, we obtained best proximity coincidence point theorems for α-Geraghty contractions in the setting of complete metric spaces by using weak P-property. Also we presented some examples to prove the validity of our results. Our results extended and unify many existing results in the literature. Moreover, in the last section as application...

In this paper, we introduce new notions of F p-contractive mapping is the set of non-self mappings and F p-proximal contractive mappings of first and second kind. Then, we generalize the best proximity point theorems and show the existence of p-best proximity points and their uniqueness by the help F p −contractions in complete metric spaces endowe...

The purpose of this paper is to introduce a new mapping for a finite family of accretive operators and introduce an iterative algorithm for finding a common zero of a finite family of accretive operators in a real reexive strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a g...

In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; (Formula presented.) where {αn}⊂(0,1). It is noted that Xu’s original iterative method can conclude only weak convergence. Consequently, we obtain the sequence {xn} g...

In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examp...

In this paper, we prove the existence and uniqueness of a coupled best proximity point for mappings satisfying the proximally coupled contraction condition in a complete ordered metric space. Further, our result provides an extension of a result due to Luong and Thuan (Comput. Math. Appl. 62 (11) (2011), 4238–4248, Nonlinear Anal. 74 (2011), 983–99...

In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well know...

In this paper, we establish the iterative algorithm for finding the solution of a general split feasibility problem (GSFPg) and show that the proposed algorithm converges strongly to solution of (GSFPg). Moreover, some numerical examples are presented to confirm our results. © 2016 by the Mathematical Association of Thailand. All rights reserved.