• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1161-1168
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• 2016

Belarbi and Dahmani [3], recently, using the Riemann-Liouville fractional integral, presented some interesting integral inequalities for the Chebyshev functional in the case of two synchronous functions. Subsequently, Dahmani et al. [5] and Sulaiman [17], provided some fractional integral inequalities. Here, motivated essentially by Belarbi and Dahmani's work [3], we aim at establishing certain (presumably) new inequalities associated with pathway fractional integral operators by using synchronous functions which are involved in the Chebychev functional. Relevant connections of the results presented here with those involving Riemann-Liouville fractional integrals are also pointed out.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.557-573
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• 2021

In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric ₂F₁(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.71-84
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• 2014

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H = 1/4.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.141-149
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• 2016

In this paper, we introduce and investigate the concept of Riemann Delta-alpha fractional integral on time scales. Many properties of this integral will be obtained.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.845-859
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• 2016

In this paper, some Hermite-Hadamard-$Fej{\acute{e}}r$ type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.

• East Asian mathematical journal
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• v.17 no.1
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• pp.135-146
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• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.587-596
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• 2021

In this article, using the concept proposed reciently by the author, of a Generalized k-Proportional Fractional Integral Operators with General Kernel, new integral inequalities are obtained for convex functions. It is shown that several known results are particular cases of the proposed inequalities and in the end new directions of work are provided.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• East Asian mathematical journal
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• v.18 no.1
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.107-114
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• 2018

We establish some new ostrowski type inequalities for MT-convex function including first order derivative via Niemann-Trouvaille fractional integral. It is interesting to mention that our results provide new estimates on these types of integral inequalities for MT-convex functions.