Page 85 - Mathematical Techniques of Fractional Order Systems

Nonlinear Fractional Order Boundary-Value Problems Chapter | 2 73

Petras, I., 2011. Fractional-Order Nonlinear Systems: Modelling, Analysis and Simulation.
Springer Verlag, Berlin.
Podlubny, I., 1999. Fractional Differential Equations. Academic Press, San Diego.
Radwan, A.G., 2013. Resonance and quality factor of the rlc fractional circuit. IEEE J. Emerg.
Selected Topics Circuits Systems 3 (3), 377 385.
Radwan, A.G., Soliman, A.M., Elwakil, A.S., 2008a. Design equations for fractional-order oscil-
lators: four practical design examples. Int. J. Circuit Theory Applicat. 36 (4), 473 492.
Radwan, A.G., Soliman, A.M., Elwakil, A.S., 2008b. International journal of circuit theory and
applications. Circ. Syst. Signal Proc. 36 (4), 473 492.
Radwan, A.G., Elwakil, A.S., Soliman, A.M., 2009a. On the generalization of second-order fil-
ters to the fractional-order domain. J. Circuits Systems Comput. 18 (2), 361 386.
Radwan, A.G., Soliman, A.M., Elwakil, A.S., Sedeek, A., 2009b. On the stability of linear sys-
tems with fractional order elements. Chaos Solitons Fractals 40, 2317 2328.
Ragb, O., Seddek, L.F., Matbuly, M., 2017. Iterative differential quadrature solutions for bratu
problem. Comput. Math. Applicat. 74, 249 257.
Sajid, M., Hayat, T., Asghar, S., 2007. Comparison between the ham and hpm solutions of thin
film flows of non-newtonian fluids on a moving belt. Nonlinear Dynamics 50 (1-2), 27 35.
Salahshour, S., Ahmadian, A., Chan, C.S., 2015. Successive approximation method for caputo q-
fractional ivps. Commun. Nonlinear Sci. Num. Simul. 24 (1-3), 153 158.
Semary, M.S., Hassan, H.N., 2015. A new approach for a class of nonlinear boundary value pro-
blems with multiple solutions. J. Associat. Arab Univ. Basic Appl. Sci. 17, 27 35.
Semary, M.S., Hassan, H.N., 2016. The homotopy analysis meyhod for q- difference equation.
Ain Shams Eng. J. In press.
Semary, M.S., AbdelMalek, H.L., Hassan, H.N., Radawn, A.G., 2016a. An optimal linear system
approximation of nonlinear fractional-order memristor-capacitor charging circuit.
Microelectron. J. 51, 58 66.
Semary, M.S., Radawn, A.G., Hassan, H.N., 2016b. Fundamentals of fractional order lti circuits
and systems: number of poles, stability, time and frequency responses. Int. J. Circuit Theory
Applicat. 44 (12), 2114 2133.
Semary, M.S., Hassan, H.N., Radwan, A.G., 2017a. Controlled picard method for solving nonlin-
ear fractional reaction-diffusion models in porous catalysts. Chem. Eng. Commun. 204 (6),
635 647.
Semary, M.S., Hassan, H.N., Radwan, A.G., 2017b. Single and dual solutions of fractional order
differential equations based on controlled picard method and simpson rule. J. Associat. Arab
Univ. Basic Appl. Sci. In press.
Soltani, L.A., Shivanian, E., Ezzati, R., 2017. Shooting homotopy analysis method: a fast
method to find multiple solutions of nonlinear boundary value problems arising in fluid
mechanics. Eng. Comput. 34 (2), 471 498.
Sun, Y.P., Liu, S.B., Keith, S., 2004. Approximate solution for the nonlinear model of diffusion
and reaction in porous catalysts by the decomposition method. Chem. Eng. J. 102, 1 10.
Valerio, D., Trujillo, J.J., Rivero, M., Machado, J.A.T., Baleanu, D., 2013. Fractional calculus: a
survey of useful formulas. Eur. Phys. J. Spec. Topics 222 (8), 1827 1846.
Vazquez-Leal, H., Rashidinia, J., Hernandez-Martinez, L., Daei-Kasmaei, H., 2015. A compari-
son of hpm, ndhpm, picard and picard-pade methods for solving michaelis-menten equation.
J. King Saud Univ. Sci. 27, 7 14.
Wazwaz, A.M., 2005. Adomian decomposition method for a reliable treatment of the bratu type
equations. Appl. Math. Comput. 166 (3), 652 663.