• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.119-125
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• 2015

In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.687-704
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• 2021

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly (α, m)-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

• 호남수학학술지
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• 제42권4호
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Kyungpook Mathematical Journal
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• 제56권4호
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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.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.257-273
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• 2010

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

• 대한수학회논문집
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• 제36권3호
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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.

• Kyungpook Mathematical Journal
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• 제56권3호
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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.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.55-66
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• 2018

By making use of the Riemann-Liouville fractional integrals, we establish further results on Chebyshev inequality. Other Steffensen integral results of the weighted Chebyshev functional are also proved. Some classical results of the paper:[ Steffensen's generalization of Chebyshev inequality. J. Math. Inequal., 9(1), (2015).] can be deduced as some special cases.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.289-295
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• 2020

Minkowski's inequality is one of the most famous inequalities in mathematics, and has many applications. In this paper, we give Minkowski's inequality for generalized variational integrals that are based on a supermultiplicative function. Our results include previous results about fractional integral inequalities of Minkowski's type.