• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.827-835
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• 2005

As a tool of measuring the irregularity of curve, fractal dimensions can be used. For an irregular function, fractional calculus are more available. However, to know its fractional differentiability which is related to its complexity is complicated one. In this paper, variants of the Hausdorff dimension and the packing dimension as well as the derivative order are defined and the relations between them are investigated so that the differentiability of fractal curve can be explained through its complexity.

• 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.33 no.1_2
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• pp.203-210
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• 2015

We consider fractional Brownian motion and FARIMA process with Gaussian innovations and show that the suitably scaled distributions of the FARIMA processes converge to fractional Brownian motion in the sense of finite dimensional distributions. We figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, d, 0) by using R/S method. Finally, we display power spectrum density of FARIMA process.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.515-521
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• 2016

This paper deals with linear impulsive differential equations with non-integer orders. We provide the explicit representation of solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions.

• East Asian mathematical journal
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• v.21 no.2
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• pp.219-231
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• 2005

This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.91-103
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• 2021

In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.315-321
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• 2010

Waring's problem deals with representing any nonconstant function in a set of functions as a sum of kth powers of nonconstant functions in the same set. Consider ${\sum}_{i=1}^p\;f_i(z)^k=z$. Suppose that $k{\geq}2$. Let p be the smallest number of functions that give the above identity. We consider Waring's problem for the set of linear fractional transformations and obtain p = k.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.