Oldham,
K. B.
, and
Spanier,
J.
, 1974, The Fractional Calculus,
Academic Press,
New York.

Podlubny,
I.
, 1999, Fractional Differential Equations, Mathematics in Science and Engineering, Vol.
198,
Academic Press,
San Diego, CA.

Miller,
K. S.
, and
Ross,
B.
, 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations,
Wiley,
New York.

Baleanu,
D.
,
Diethelm,
K.
,
Scalas,
E.
, and
Trujillo,
J.
, 2012, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos),
World Scientific Publishing Company, Singapore.

Adomian,
G.
, and
Rach,
R.
, 1996, “
Modified Adomian Polynomials,” Math. Comput. Modell.,
24(11), pp. 39–46.

[CrossRef]
Adomian,
G.
, 1988, “
A Review of the Decomposition Method in Applied Mathematics,” J. Math. Anal. Appl.,
135(2), pp. 501–544.

[CrossRef]
Daftardar-Gejji,
V.
, and
Jafari,
H.
, 2005, “
Adomian Decomposition: A Tool for Solving a System of Fractional Differential Equations,” J. Math. Anal. Appl.,
301(2), pp. 508–518.

[CrossRef]
Wazwaz,
A.-M.
, 2006, “
The Modified Decomposition Method for Analytic Treatment of Differential Equations,” Appl. Math. Comput.,
173(1), pp. 165–176.

[CrossRef]
Deeba,
E.
, and
Khuri,
S.
, 1996, “
A Decomposition Method for Solving the Nonlinear Klein-Gordon Equation,” J. Comput. Phys.,
124(2), pp. 442–448.

[CrossRef]
Yusufoğlu,
E.
, 2008, “
The Variational Iteration Method for Studying the Klein-Gordon Equation,” Appl. Math. Lett.,
21(7), pp. 669–674.

[CrossRef]
Jafari,
H.
,
Tajadodi,
H.
, and
Baleanu,
D.
, 2013, “
A Modified Variational Iteration Method for Solving Fractional Riccati Differential Equation by Adomian Polynomials,” Fractional Calculus Appl. Anal.,
16(1), pp. 109–122.

Kurulay,
M.
, 2012, “
Solving the Fractional Nonlinear Klein–Gordon Equation by Means of the Homotopy Analysis Method,” Adv. Differ. Equations,
2012(1), p. 187.

[CrossRef]
Golbabai,
A.
, and
Sayevand,
K.
, 2011, “
Analytical Modelling of Fractional Advection-Dispersion Equation Defined in a Bounded Space Domain,” Math. Comput. Modell.,
53(9–10), pp. 1708–1718.

[CrossRef]
Jafari,
H.
,
Tajadodi,
H.
, and
Baleanu,
D.
, 2014, “
Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Fractional Evolution Equations,” ASME J. Comput. Nonlinear Dyn.,
9(2), p. 021019.

[CrossRef]
Firoozjaee,
M.
,
Yousefi,
S.
,
Jafari,
H.
, and
Baleanu,
D.
, 2015, “
On a Numerical Approach to Solve Multi-Order Fractional Differential Equations With Initial/Boundary Conditions,” ASME J. Comput. Nonlinear Dyn.,
10(6), p. 061025.

[CrossRef]
Golbabai,
A.
, and
Nikan,
O.
, 2015, “
Application of the RBF Meshless Approach for Solving Fractional Order Differential Equations,” J. Comput. Complex Appl.,
1(2), pp. 64–78.

Evirgen,
F.
, and
Ozdemir,
N.
, 2011, “
Multistage Adomian Decomposition Method for Solving NLP Problems Over a Nonlinear Fractional Dynamical System,” ASME J. Comput. Nonlinear Dyn.,
6(2), p. 021003.

[CrossRef]
Bekir,
A.
, 2009, “
New Exact Travelling Wave Solutions of Some Complex Nonlinear Equations,” Commun. Nonlinear Sci. Numer. Simul.,
14(4), pp. 1069–1077.

[CrossRef]
Kumar,
S.
,
Yildirim,
A.
,
Khan,
Y.
,
Jafari,
H.
,
Sayevand,
K.
, and
Wei,
L.
, 2012, “
Analytical Solution of Fractional Black-Scholes European Option Pricing Equation by Using Laplace Transform,” J. Fractional Calculus Appl.,
2(8), pp. 1–9.

Sejdic,
E.
,
Djurovic,
I.
, and
Stankovic,
L.
, 2011, “
Fractional Fourier Transform as a Signal Processing Tool: An Overview of Recent Developments,” Signal Process.,
91(6), pp. 1351–1369.

[CrossRef]
Miurs,
M.
, 1978, Backlund Transformation,
Springer,
Berlin.

Daftardar-Gejji,
V.
, and
Jafari,
H.
, 2006, “
An Iterative Method for Solving Nonlinear Functional Equations,” J. Math. Anal. Appl.,
316(2), pp. 753–763.

[CrossRef]
Golmankhaneh,
A. K.
,
Khatuni,
T.
,
Porghoveh,
N. A.
, and
Baleanu,
D.
, 2012, “
Comparison of Iterative Methods by Solving Nonlinear Sturm–Liouville, Burgers and Navier–Stokes Equations,” Cent. Eur. J. Phys.,
10(4), pp. 966–976.

Golmankhaneh,
A. K.
,
Golmankhaneh,
A. K.
, and
Baleanu,
D.
, 2011, “
On Nonlinear Fractional Klein–Gordon Equation,” Signal Process.,
91(3), pp. 446–451.

[CrossRef]
Hariharan,
G.
, 2013, “
Wavelet Method for a Class of Fractional Klein–Gordon Equations,” ASME J. Comput. Nonlinear Dyn.,
8(2), p. 021008.

[CrossRef]
Duan,
J.
, 2015, “
The Adomian Polynomials and the New Modified Decomposition Method for BVPs of Nonlinear ODEs,” Math. Comput.,
4(1), pp. 1–6.

[CrossRef]
Duan,
J.-S.
, 2011, “
New Recurrence Algorithms for the Nonclassic Adomian Polynomials,” Comput. Math. Appl.,
62(8), pp. 2961–2977.

[CrossRef]
Duan,
J.-S.
, 2011, “
New Ideas for Decomposing Nonlinearities in Differential Equations,” Appl. Math. Comput.,
218(5), pp. 1774–1784.

[CrossRef]
Zeng,
Y.
, 2016, “
Approximate Solutions of Three Integral Equations by the New Adomian Decomposition Method,” J. Comput. Complex Appl.,
2(1), pp. 38–43.

Abdelrazec,
A.
, and
Pelinovsky,
D.
, 2011, “
Convergence of the Adomian Decomposition Method for Initial-Value Problems,” Numer. Methods Partial Differ. Equations,
27(4), pp. 749–766.

[CrossRef]
Bhalekar,
S.
, and
Daftardar-Gejji,
V.
, 2011, “
Convergence of the New Iterative Method,” Int. J. Differ. Equations,
2011, p. 989065.