Orders of Solutions of Fractional Differential Equation in Complex Domain

Authors : Hamıd BEDDANI

Pages : 70-77

View : 38 | Download : 9

Publication Date : 2022-11-01

Article Type : Research Paper

Abstract :We consider the fractional differential equation $^{c}D_{z}^{\alpha }f^{\prime }insert ignore into journalissuearticles values(z);+Ainsert ignore into journalissuearticles values(z);^{c}D_{z}^{\alpha }finsert ignore into journalissuearticles values(z);+Binsert ignore into journalissuearticles values(z);finsert ignore into journalissuearticles values(z);=0$, where $^{c}D_{z}^{\alpha }$\ be the Caputo fractional derivative of orders $0<\alpha \leq 1$, and $z$\ is complex number, $Ainsert ignore into journalissuearticles values(z);,Binsert ignore into journalissuearticles values(z);$\ be entire functions. We will find conditions on $Ainsert ignore into journalissuearticles values(z);,Binsert ignore into journalissuearticles values(z);$\ which will guarantee that every solution $f\not\equiv 0$ of the equation will have infinite order.
Keywords : The fractional derivative, entire function, infinite order, complex domain

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