A New Approach to Fractional Derivatives

Authors

  • Ibrahim M. Alghrouz

Keywords:

Approach, Fractional Derivatives, Mathematics, Function, Power series,

Abstract

A derivative of a function of order , for any real number ( called a fractional derivative) is the subject of this paper. In this paper a new defi­nition of the fractional derivative of order of a function is given. This new definitionwilldependontheformalpowerseriessummation.Weusedthis new definitiontofindthefractionalderivativeoftheconstantfunctionsand the polynomials. The result was the same result by using the known definitionsoffractionalderivativesuntilnow.Also,weprovedpropertiesofthe fractional derivative. Finally, we conjecture that the fractional derivative of order of the exponential function is the exponential function and this will help us in findingthefractionalderivativesofthetrigonometricfunctions and hyperbolic functions.

The purpose of this research is to findaneasywaytoderivethefractionalderivatives for the functions, since every differentiable function can be rep­resented by power series expansion, even if the radius of convergence of the power series is 0, we believe that this method will give nice results which can be used in the application.

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Published

2017-06-12

How to Cite

M. Alghrouz, I. (2017). A New Approach to Fractional Derivatives. Journal of Al-Quds Open University for Humanities and Social Studies, (10). Retrieved from https://journals.qou.edu/index.php/jrresstudy/article/view/828

Issue

No. 10 (2007): العدد العاشر-ربيع الأول 1428ه/ نيسان 2007م

Section

Research Papers

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