Int. J. Appl. Comput. Math (2018) 4:20
An Efﬁcient Approach of Homotopic Asymptotic for
System Differential Equations of Non Integer Order
· B. Agheli
© Springer (India) Private Ltd., part of Springer Nature 2017
Abstract The momentous objective of this paper is to using a method with a free parameter
which named optimum asymptotic homotopic method for ﬁnding solution of system differ-
ential equations featuring fractional derivative. To better understand the methodology and
view its advantages compared to similar examples are presented.
Keywords System differential equations · Optimum homotopic asymptotic · Caputo
Mathematics Subject Classiﬁcation 93C20 · 65F10 · 26A33
Fractional arithmetic and fractional differential equations appeared in many disciplines,
including medicine , economics , dynamical problems [3,4], chemistry , mathe-
matical physics [6,7], trafﬁc model  and ﬂuid ﬂow [9,10] and so on.
Scholars and researchers are invited to study books that have been written to better under-
stand the concept of fractional arithmetic [11,12].
In order to ﬁnd the approximate solution for system differential equations with fractional
derivative that we explored in this paper is presented as follows:
(x , t) + N
(x , t), u
(x , t)
(x , t), n − 1 <μ≤ n, j = 1, 2, (1)
Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran