• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.907-925
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• 2012

In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\acute{o}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.279-295
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• 2019

In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.537-555
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• 2015

This paper is concerned with the existence of solutions to the following fractional differential inclusion $$\{-{\frac{d}{dx}}\(p_0D^{-{\beta}}_x(u^{\prime}(x)))+q_xD^{-{\beta}}_1(u^{\prime}(x))\){\in}{\partial}F_u(x,u),\;x{\in}(0,1),\\u(0)=u(1)=0,$$ where $_0D^{-{\beta}}_x$ and $_xD^{-{\beta}}_1$ are left and right Riemann-Liouville fractional integrals of order ${\beta}{\in}(0,1)$ respectively, 0 < p = 1 - q < 1 and $F:[0,1]{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants p and q, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.601-617
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• 2017

We give a function associated with generalized Ostrowski type inequality and its integral representation for local fractional calculus. Then, using this function and its integral representation, we establish several inequalities of generalized Ostrowski type for twice local fractional differentiable functions. We also consider some special cases of the main results which are further applied to a concrete function to yield two interesting inequalities associated with two generalized means.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.297-314
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• 2024

Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for s-convex function are also given. Furthermore, applications to some special means, quadrature formula, and q-digamma functions are presented.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.165-171
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• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.115-129
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• 2016

Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. [9] evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, $Erd\acute{e}lyi$-Kober and Saigo operators, associated with multivariable H-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-436
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• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.31-39
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• 2009

Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.341-349
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• 2019

This paper is concerned to investigate M-Wright function, which was earlier known as transcendental function of the Wright type. M-Wright function is a special case of the Wright function given by British mathematician (E.Maitland Wright) in 1933. We have explored the cosequences of Riemann-Liouville Integral and Differential operators on M-Wright function. We have also evaluated integral transforms of the M-Wright function.