Thermal Analysis of a Casson Boundary Layer Flow over a Penetrable Stretching Porous Wedge
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Journal of Mathematics is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.
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Chief Editor, Professor Jen-Chih Yao, is currently based at Zhejiang Normal University in China. His current research includes dynamic programming, mathematical programming, and operations research.
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More articlesA Second-Order Finite-Difference Method for Derivative-Free Optimization
In this paper, a second-order finite-difference method is proposed for finding the second-order stationary point of derivative-free nonconvex unconstrained optimization problems. The forward-difference or the central-difference technique is used to approximate the gradient and Hessian matrix of objective function, respectively. The traditional trust-region framework is used, and we minimize the approximation trust region subproblem to obtain the search direction. The global convergence of the algorithm is given without the fully quadratic assumption. Numerical results show the effectiveness of the algorithm using the forward-difference and central-difference approximations.
Study of Nonlinear Second-Order Differential Inclusion Driven by a Laplacian Operator Using the Lower and Upper Solutions Method
In this paper, we study a second-order differential inclusion under boundary conditions governed by maximal monotone multivalued operators. These boundary conditions incorporate the classical Dirichlet, Neumann, and Sturm–Liouville problems. Our method of study combines the method of lower and upper solutions, the analysis of multivalued functions, and the theory of monotone operators. We show the existence of solutions when the lower solution and the upper solution are well ordered. Next, we show how our arguments of proof can be easily exploited to establish the existence of extremal solutions in the functional interval . We also show that our method can be applied to the periodic case.
A Convergent Legendre Spectral Collocation Method for the Variable-Order Fractional-Functional Optimal Control Problems
In this paper, a numerical method is applied to approximate the solution of variable-order fractional-functional optimal control problems. The variable-order fractional derivative is described in the type III Caputo sense. The technique of approximating the optimal solution of the problem using Lagrange interpolating polynomials is employed by utilizing the shifted Legendre–Gauss–Lobatto collocation points. To obtain the coefficients of these interpolating polynomials, the problem is transformed into a nonlinear programming problem. The proposed method offers a significant advantage in that it does not require the approximation of singular integral. In addition, the matrix differentiation is calculated accurately and efficiently, overcoming the difficulties posed by variable-order fractional derivatives. The convergence of the proposed method is investigated, and to validate the effectiveness of our proposed method, some examples are presented. We achieved an excellent agreement between numerical and exact solutions for different variable orders, indicating our method’s good performance.
On a Perturbed Risk Model with Time-Dependent Claim Sizes
We consider a risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the inter-claim times. We study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. Integro-differential equations and Laplace transforms satisfied by the Gerber–Shiu functions are obtained. Then, it is shown that the expected discounted penalty functions satisfy defective renewal equations. Explicit expressions can be obtained for exponential claim sizes. Finally, a numerical example is provided to measure the impact of the various dependence parameters in the risk model on the ruin probabilities.
On Partial Exact Controllability of Fractional Control Systems in Conformable Sense
In this work, we investigate the partial exact controllability of fractional semilinear control systems in the sense of conformable derivatives. Initially, we establish the existence and uniqueness of the mild solution for this type of fractional control systems. Then, by employing a contraction mapping principle, we obtain sufficient conditions for the conformable fractional semilinear system to be partially exactly controllable, assuming that its associated linear part is partially exactly controllable. To demonstrate the efficacy of the theoretical findings, a typical example is provided at the end.
Distance-Based Fractional Dimension of Certain Wheel Networks
Metric dimension is one of the distance-based parameters which are used to find the position of the robot in a network space by utilizing lesser number of notes and minimum consumption of time. It is also used to characterize the chemical compounds. The metric dimension has a wide range of applications in the field of computer science such as integer programming, radar tracking, pattern recognition, robot navigation, and image processing. A vertex in a network resolves the adjacent pair of vertices if attains an unequal distance from end points of . A local resolving neighbourhood set is a set of vertices of which resolve . A mapping is called local resolving function of if for any adjacent pair of vertices of of and the minimal value of for all local resolving functions of is called local fractional metric dimension of . In this paper, we have studied the local fractional metric dimension of wheel-related networks such as web-wheel network, subdivision of wheel network, line network of subdivision of wheel network, and double-wheel network and also examined their boundedness.