In this paper, we obtain the existence results for positive solutions of a class of multi-point boundary value problems for p-Laplacian fractional differential equations with singular source terms by using the fixed p...
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In this paper, we obtain the existence results for positive solutions of a class of multi-point boundary value problems for p-Laplacian fractional differential equations with singular source terms by using the fixed point theorem for mixed monotone operators. Furthermore, some examples are given to illustrate our results. (C) 2019 Elsevier B.V. All rights reserved.
In this work, an efficient computational method is proposed for solving the linear multi-point boundary value problems (MBVPs). Our approach depends mainly on of the least squares approximation method, the Lagrange-mu...
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In this work, an efficient computational method is proposed for solving the linear multi-point boundary value problems (MBVPs). Our approach depends mainly on of the least squares approximation method, the Lagrange-multiplier method and the residual error function technique. With the proposed scheme, we handle the numerical solutions of the linear MBVPs in a straightforward manner. Firstly, the given linear MBVP is reduced to a linear system of algebraic equations, and the coefficients of the approximate polynomial solution of the problem are determined by solving this system. Secondly, a linear boundaryvalue problem related to the error function of the approximate solution is constructed, and error estimation is presented for the suggested method. The convergence of the approximate solution is proved. The reliability and efficiency of the proposed approach are demonstrated by some numerical examples. (C) 2017 Elsevier Inc. All rights reserved.
In this paper, we investigate the existence and uniqueness of positive solutions of a kind of multi-point boundary value problems for nonlinear fractional differential equations with p-Laplacian operator using the Ban...
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In this paper, we investigate the existence and uniqueness of positive solutions of a kind of multi-point boundary value problems for nonlinear fractional differential equations with p-Laplacian operator using the Banach contraction mapping principle. Furthermore, some examples are given to illustrate our results.
In this paper, we present an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. We first analyze the strong order of convergence of the underlying multiple shooting method. We t...
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In this paper, we present an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. We first analyze the strong order of convergence of the underlying multiple shooting method. We then proceed to describe the proposed strategy to adaptively choose the location of shooting points. We analyze the effect of method parameters on the performance of the overall scheme using a benchmark linear two-point stochastic boundaryvalue problem. We illustrate the effectiveness of this approach on several (one and two dimensional) test problems by comparing our results with other non-adaptive alternative techniques proposed in the literature.
In this paper, we investigate the existence and uniqueness of solutions to the coupled system of nonlinear fractional differential equations {-D(0+)(v1)y(1)(t) = lambda(1)a(1)(t)f(y(1)(t), y(2)(t)), -D(0+)(v2)y(2)(t) ...
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In this paper, we investigate the existence and uniqueness of solutions to the coupled system of nonlinear fractional differential equations {-D(0+)(v1)y(1)(t) = lambda(1)a(1)(t)f(y(1)(t), y(2)(t)), -D(0+)(v2)y(2)(t) = lambda(2)a(2)(t)g(y(1)(t),y(2)(t)), where D-0+(v) is the standard Riemann-Liouville fractional derivative of order v, t is an element of (0, 1), v(1), v(2) is an element of (n - 1, n] for n > 3 and n is an element of N, and lambda(1), lambda(2) > 0, with the multi-pointboundaryvalue conditions: y(1)(i) (0) = 0 = y(2)(i) (0), 0 <= i <= n - 2;D(0+)(beta)y(1)(1) = Sigma(m-2)(i=1) b(i)D(0+)(beta)y(1)(xi(i));D(0+)(beta)y(2)(1) = Sigma(m-2)(i=1) b(i)D(0+)(beta)y(2)(xi(i)), where n -2 < beta < n - 1, 0 < xi(1) < xi(2) < ... = 0 (i = 1,2,..., m-2) with rho(1) := Sigma(m-2)(i=1) b(i)xi(v1-beta-1)(i) < 1, and rho(2) := Sigma(m-2)(i=1) b(i)xi(v2-beta-1)(j) < 1. Our analysis relies on the Banach contraction principle and Krasnoselskii's fixed point theorem.
In this paper, we obtain the existence of infinitely many classical solutions to the multi-pointboundaryvalue system [GRAPHICS] Our analysis is based on critical point theory.
In this paper, we obtain the existence of infinitely many classical solutions to the multi-pointboundaryvalue system [GRAPHICS] Our analysis is based on critical point theory.
This paper focuses on developing an efficient numerical approach based on Taylor-wavelets for solving three-point (nonlocal) singular boundaryvalueproblems. A special case of the considered problem, with strongly no...
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This paper focuses on developing an efficient numerical approach based on Taylor-wavelets for solving three-point (nonlocal) singular boundaryvalueproblems. A special case of the considered problem, with strongly nonlinear source term, arises in thermal explosion in a cylindrical reactor. The existence of a unique solution is thoroughly discussed for the considered problem. To establish the current method, an equivalent integral equation is constructed for the original problem to overcome the singularity at the origin. The evaluation of derivatives appearing in the model is also avoided in this way. Moreover, this scheme skips the integrals while reducing them into a system of nonlinear algebraic equations. Unlike other methods, this new approach does not require any linearization, discretization, perturbation, or evaluation of nonlinear terms separately. To the best of our knowledge, this is the first application of the wavelet-based method to the considered problem. The formulation of the proposed method is further supported by its convergence and error analysis. Some numerical examples are solved to validate the efficiency and robustness of the proposed method. Further, the computational convergence rate (COR) is reported for the first few examples to assist the obtained numerical solution. Moreover, the obtained numerical results are compared with those of existing techniques in the literature.
multi-point boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering. In this work, our goal is to obtain numerically the approximate s...
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multi-point boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering. In this work, our goal is to obtain numerically the approximate solution of these problems by using the Sinc-collocation method. Some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce the computation of solution of multi-point boundary value problems to some algebraic equations. It is well known that the Sinc procedure converges to the solution at an exponential rate. Numerical examples are included to demonstrate the validity and applicability of the new technique. (C) 2011 Elsevier B.V. All rights reserved.
Results on the existence of solutions of a integral type boundaryvalue problem for the multiple term fractional differential equation with the nonlinearity depending on D(0+)(alpha)x are established. The analysis rel...
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Results on the existence of solutions of a integral type boundaryvalue problem for the multiple term fractional differential equation with the nonlinearity depending on D(0+)(alpha)x are established. The analysis relies on the nonlinear alternative theory. Corollaries and examples are given to illustrate the efficiency of the main theorems. (c) 2011 Elsevier Ltd. All rights reserved.
In this work, multi-point boundary value problems are considered. These problems have important roles in the modelling of various problems in physics and engineering. Although numerous works have been carried out on t...
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In this work, multi-point boundary value problems are considered. These problems have important roles in the modelling of various problems in physics and engineering. Although numerous works have been carried out on the existence and uniqueness to the solution of these problems, the numerical or analytical methods are not established for solving them. In this paper the well-known He's variational iteration method is applied for solving the multi-point boundary value problems. The method is modified and the results are shown using some test problems. These results show the efficiency of the new approach.
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