Page 83 - Mathematical Techniques of Fractional Order Systems

Nonlinear Fractional Order Boundary-Value Problems Chapter | 2 71

Abbasbandy, S., Shirzadi, A., 2011. A new application of the homotopy analysis method: solving
the sturm-liouville problems. Commun. Nonlinear Sci. Num. Simul. 16 (1), 112 126.
Abbasbandy, S., Shivanian, E., 2010. Prediction of multiplicity of solutions of nonlinear bound-
ary value problems: novel application of homotopy analysis method. Commun. Nonlinear
Sci. Num. Simul. 15 (12), 3830 3846.
Abbasbandy, S., Shivanian, E., 2011. Predictor homotopy analysis method and its application to
some nonlinear problems. Commun. Nonlinear Sci. Num. Simul. 16 (6), 2456 2468.
Abbasbandy, S., Magyari, E., Shivanian, E., 2009. The homotopy analysis method for multiple
solutions of nonlinear boundary value problems. Commun. Nonlinear Sci. Num. Simul. 14
(9-10), 3530 3536.
Alomari, A., Awawdeh, F., Tahat, N., Ahmad, F.B., Shatanawi, W., 2013. Multiple solutions for
fractional differential equations: analytic approach. Appl. Math. Comput. 219, 8893 8903.
Arqub, O.A., El-Ajou, A., Zhour, Z.A., Momani, S., 2014. Multiple solutions of nonlinear
boundary value problems of fractional order: a new analytic iterative technique. Entropy 16,
471 493.
Atkinson, K.E., 1989. An Introduction to Numerical Analysis. John Wiley & Sons, Hoboken.
Azar, A.T., Vaidyanathan, S., Ouannas, A., 2017. Fractional Order Control and Synchronization
of Chaotic Systems. Studies in Computational Intelligence, Vol. 688. Springer-Verlag,
Germany.
Azarnavid, B., Parvaneh, F., Abbasbandy, S., 2015. Picard-reproducing kernel hilbert space
method for solving generalized singular nonlinear lane-emden type equations. Math. Model.
Anal. 20 (6), 754 767.
Barletta, A., 1999. Laminar convection in a vertical channel with viscous dissipation and buoy-
ancy effects. Int. Commun. Heat Mass Transfer 26, 153 164.
Barletta, A., Magyari, E., Keller, B., 2005. Dual mixed convection flows in a vertical channel.
Int. J. Heat Mass Transfer 48, 4835 4845.
Bataineh, A., Noorani, M., Hashim, I., 2007. Solutions of time-dependent emden fowler type
equations by homotopy analysis method. Phys. Lett. A 371 (1 2), 72 82.
Chang, M.H., 2005. A decomposition solution for fins with temperature dependent surface heat
flux. Int. J. Heat Mass Transfer 48 (9), 1819 1824.
Chowdhury, M., Hashim, I., 2008. Analytical solutions to heat transfer equations by homotopy-
perturbation method revisited. Phys. Lett. A 372, 1240 1243.
Das, S., Pan, I., 2012. Fractional Order Signal Processing: Introductory Concepts and
Applications. Springer, New York.
Don, W.S., Solomonoff, A., 1995. Accuracy and speed in computing the cheby-shev collocation
derivative. SIAM J. Sci. Comput. 16, 1253 1268.
El-Sayed, A.M.A., Hashem, H.H.G., Ziada, E.A.A., 2014. Picard and adomian decomposition
methods for a quadratic integral equation of fractional order. Comput. Appl. Math. 33 (1),
95 109.
Ellery, A., Simpson, M., 2011. An analytical method to solve a general class of nonlinear reac-
tive transport models. Chem. Eng. J. 169, 313 318.
Fouda, M.E., Radwan, A.G., 2015. Fractional-order memristor response under dc and periodic
signals. Circ. Syst. Signal Proc. 34 (3), 961 970.
Freeborn, T.J., Maundy, B., Elwakil, A.S., 2013. Cole impedance extractions from the step-
response of a current excited fruit sample. Comput. Electron. Agric. 98, 100 108.
Ganji, D.D., 2006. The application of he’s homotopy perturbation method to nonlinear equations
arising in heat transfer equations by optimal homotopy analysis method. Phys. Lett. A 355,
337 341.