• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.269-282
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• 2007

In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.425-443
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• 2012

Sufficient conditions for the existence of at least one solution of a class of multi-point boundary value problems of the fractional differential equations at resonance are established. The main theorem generalizes and improves those ones in [Liu, B., Solvability of multi-point boundary value problems at resonance(II), Appl. Math. Comput., 136(2003)353-377], see Remark 2.3. An example is presented to illustrate the main results.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.131-143
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• 2002

In this paper hi-criterion quadratic fractional generalized solid transportation problem is studied. An algorithm is developed to obtain the time-cost trade-off pairs and hence identifies the optimum trade-off pairs giving the equal priority to both time and cost. A numerical example is illustrated to support the algorithm.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.1-11
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• 2005

Making use of the multidimensional fractional calculus operators introduced in [20], this paper gives the images under these operators of the celebrated Fox's H-function. Special cases are briefly point out, and some of the results are also studied on general spaces of functions $M_{\lambda}(R_{+}^n)$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.361-376
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• 2005

Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.105-126
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• 2007

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.1-23
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• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.695-706
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• 1999

When fractional factorial experiments contain some infeasible treatment combinations called debarred combinations we should construct experimental designs so that those debarred combinations are to be excluded by selecting defining contrasts appropriately. By applying Franklin(1995)'s procedure for selecting defining contrasts to Cheng and Li(1993)'s method this paper presents a method of selecting defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1011-1020
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• 2021

In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

• Current Optics and Photonics
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• v.7 no.2
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• pp.127-135
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• 2023

Radially polarized beams with the ability to generate a sub-wavelength sized spot in a longitudinal field provides significant applications in microscopic imaging, optical tweezers, lithography and so on. However, this excellent property can also be achieved based on conventional circularly polarized beams. Here, we demonstrate its ability to create a strong longitudinal field by comparing the tight focusing characteristics of fractional-order vortex modulated radial polarized and left-handed circular polarized Bessel-Gauss beams. Additionally, the possibility of generating arbitrary fractional-order vortex modulated Bessel-Gauss beams with a strong longitudinal field is demonstrated. A special modulation method of left-handed circularly polarized Bessel-Gauss beams modulated by a fractional-order vortex is adopted creatively and a series of regulation laws are obtained. Specifically, the fractional-order phase modulation parameter n can accurately control the number of optical lobes. The ratio of the pupil radius to the incident beam waist β₁ can control the radius of the optical lobes. The first-order Bessel function amplitude modulation parameter β₂ can control the number of layers of optical lobes. This work not only adds a new modulation method for optical micromanipulation and optical communication, but also enriches the research on fractional vortex beams which has very important academic significance.