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On Solution of Viscoelastic FractionalDifferential Equation

المؤلف: Ass. proofesor Saad Naji Al-Azawi
ﺎﻠﻤﺠﻟﺓ: Al-Fatih journal مجلة الفتح ISSN: 87521996 السنة: 2008 المجلد: 4 الاصدار: 35 الصفحات: 150-166
الجامعة: Diyala University جامعة ديالى - جامعة ديالى

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الخلاصة

Fractional calculus is an old and new branch of mathematics with a long history. It’s early beginning was in 1695 when G. W. Leibniz wrote a letter from Hanover, Germany, September 30, 1695 to G. A. L’Hopital said that which is an apparent paradox and this was found in volume 2, pp.301-302, Olms Verlag, Hildesheim, Germany 1962 and first published in 1849. After two years Leibinz wrote a letter to Wallis to discuss infinite product of and in this letter Leibinz mentioned to differential calculus and used to derivative of order . For most details of historical background see [1,5].
The first application of fractional calculus is due to Abel in 1823 in solving an integral equation which arises in the tautochrone problem which is sometimes called isochrone problem and it is of finding the shape of a fractionless wire lying in a vertical plane such that the time of slide of a bead placed on the wire slides to the lowest point of the wire in the same time regardless of where the bead is placed.

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