• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.503-520
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• 2022

We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• 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 Information Management
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• v.39 no.3
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• pp.95-113
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• 2008

In todays environment in which scientific technologies are changing very fast than ever, companies have to monitor and search emerging technologies to gain competitiveness. Actually many nations try to do that. Most of them use Dephi approach based on experts review as a searching method. But experts review has been criticised for probability of inclination and its derivative problems in the sense that it is accomplished only by expert's subjectivity. To overcome such problems, we used Scientometric Method for identifying emerging technology that had been done by Delphi as a rule. We made three particular efforts in order to improve the Quality of the result. Firstly, we selected one alternative database between SCI and Scopus hoping to see evenly-distributing results in wide fields on the front burner. Secondly we used Fractional citation counting in counting citation number in the stage of linear regression analysis. Lastly, we verified Scientometric result with experts opinions to minimize probable errors in a Scientometric research. As a result, we derived 290 emerging technologies from Scientometric analysis with Scopus Database, and visualized them on 2-dimension map with data mining system named KnowledgeMatrix which was developed by KISTI.