2017arXiv (Cornell University)Open access

A new Generalized fractional derivative and integral

Abdullah Akkurt, M. Esra Yıldırım, Hüseyin Yıldırım

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Abstract

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem. We give some examples.

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What this paper is about

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem. We give some examples.

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Available abstract

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem. We give some examples.

Key concepts: Fractional calculus, Derivative (finance), Mathematics, Applied mathematics, Economics, Financial economics

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