An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative | Zendy

H. R. Marasi | Zendy; A. Soltani Joujehi | Zendy; Hassen Aydi | Zendy

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An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

Author(s) -

H. R. Marasi,

A. Soltani Joujehi,

Hassen Aydi

Publication year - 2021

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2021/6624861

Subject(s) - mathematics , fractional calculus , invertible matrix , extension (predicate logic) , uniqueness , derivative (finance) , picard–lindelöf theorem , initial value problem , mathematical analysis , differential equation , kernel (algebra) , pure mathematics , fixed point theorem , computer science , financial economics , economics , programming language

In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.

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