• Korean Journal of Mathematics
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• v.29 no.2
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.191-200
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• 2017

The theory of $u_0-positive$ operators is applied to obtain smallest eigenvalue comparison results for right focal boundary value problems of Atici-Eloe fractional difference equations.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.657-668
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• 2022

In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces $e^{\varsigma}_{0,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ and $e^{\varsigma}_{c,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ are also elaborate. In addition to this, we determine the 𝛼-, 𝛽- and 𝛾- duals of these spaces.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Journal of Korean Society for Atmospheric Environment
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• v.33 no.5
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• pp.497-514
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• 2017

This study quantitatively analyzes the effects of emission inventory choices on the simulated particulate matter (PM) concentrations and the domestic/foreign contributions in the Seoul Metropolitan Area (SMA) with an air quality forecasting system. The forecasting system is composed of Weather Research and Forecasting (WRF)-Sparse Matrix Operator Kernel Emissions (SMOKE)-Community Multi-Scale Air Quality (CMAQ). Different domestic and foreign emission inventories were selectively adopted to set up four sets of emissions inputs for air quality simulations in this study. All modeling cases showed that model performance statistics satisfied the criteria levels (correlation coefficient >0.7, fractional error <50%) suggested by previous studies. Notwithstanding the apparently good model performance of total PM concentrations by all emission cases, annual average concentrations of simulated total PM concentrations varied up to $20{\mu}g/m^3$ (160%) depending on the combination of emission inventories. In detail, the difference in simulated annual average concentrations of the primary PM coarse (PMC) was up to $25.2{\mu}g/m^3$ (6.5 times) compared with other cases. Furthermore, model performance analyses on PM species showed that the difference in the simulated primary PMC led to gross model overestimation in general, which indicates that the primary PMC emissions need to be improved. The contribution analysis using model direct outputs indicated that the domestic contributions to the annual average PM concentrations in the SMA vary from 44% to 67%. To account for the uncertainty of the simulated concentration, the contribution correction factor method proposed by Bae et al. (2017) was applied, which resulted in converged contributions(from 48% to 57%). We believe this study shows that it is necessary to improve the simulated concentrations of PM components in order to enhance the accuracy of the forecasting model. It is deemed that these improvements will provide more accurate contribution results.