[1]
|
Waleed, H. (2013) Solving nth Order Integro Differential Equations Using the Combined Laplace Transform Adomian Decomposition Method. Applied Mathematics, 4, 882-886.
|
[2]
|
Weerakoon, S. (1994) Application of Sumudu Transform to Partial Differential Equations. International Journal of Mathematical Education in Science and Technology, 25, 277-283. https://doi.org/10.1080/0020739940250214
|
[3]
|
Belgacem, F.B.M. (2010) Sumudu Transform Applications to Bessel Functions and Equations. Applied Mathematical Sciences, 4, 3665-3686.
|
[4]
|
Gupta, V.G., Sharma, B. and Belgacem, F.B.M. (2011) On the Solutions of Generalized Fractional Kinetic Equations. Applied Mathematical Sciences, 5, 899-910.
|
[5]
|
Katatbeh, Q.D. and Belgacem, F.B.M. (2011) Applications of the Sumudu Transform to Fractional Differential Equations. Nonlinear Studies, 18, 99-112.
|
[6]
|
Guerrero, F., Santonja, F.J. and Villanueva, R.J. (2013) Solving a Model for the Evolution of Smoking Habit in Spain with Homotopy Analysis Method. Nonlinear Analysis: Real World Applications, 14, 549-558.
https://doi.org/10.1016/j.nonrwa.2012.07.015
|
[7]
|
Jafari, H. and Firoozjaee, M.A. (2010) Multistage Homotopy Analysis Method for Solving Non-Linear Riccati Differential Equations. International Journal of Research and Reviews in Applied Sciences, 4, 128-132.
|
[8]
|
Elsaid, A. (2011) Homotopy Analysis Method for Solving a Class of Fractional Partial Differential Equations. Communications in Nonlinear Science and Numerical Simulation, 16, 3655-3664.
https://doi.org/10.1016/j.cnsns.2010.12.040
|
[9]
|
Mohyud-Din, S.T., Yldrm, A. and Ylkl, E. (2012) Homotopy Analysis Method for Space- and Time-Fractional Kdv Equation. International Journal of Numerical Methods for Heat & Fluid Flow, 22, 928-941.
https://doi.org/10.1108/09615531211255798
|
[10]
|
Das, N., Singh, R., Wazwaz, A.M. and Kumar, J. (2016) An Algorithm Based on the Variational Iteration Technique for the Bratu-Type and the Lane-Emden Problems. Journal of Mathematical Chemistry, 54, 527-551.
https://doi.org/10.1007/s10910-015-0575-6
|
[11]
|
Mistry, P.R. and Pradhan, V.H. (2015) Approximate Analytical Solution of Non-Linear Equation in One Dimensional Instability Phenomenon in Homogeneous Porous Media in Horizontal Direction by Variational Iteration Method. Procedia Engineering, 127, 970-977. https://doi.org/10.1016/j.proeng.2015.11.445
|
[12]
|
Duan, J.S., Rach, R. and Wazwaz, A.M. (2015) Steady-State Concentrations of Carbon Dioxide Absorbed into Phenyl Glycidyl Ether Solutions by the Adomian Decomposition Method. Journal of Mathematical Chemistry, 53, 1054-1067.
https://doi.org/10.1007/s10910-014-0469-z
|
[13]
|
Lu, L., Duan, J. and Fan, L. (2015) Solution of the Magnetohydrodynamics Jeffery-Hamel FFOW Equations by the Modiffed Adomian Decomposition Method. Advances in Applied Mathematics and Mechanics, 7, 675-686.
https://doi.org/10.4208/aamm.2014.m543
|
[14]
|
Ma, H.C., Yao, D.D. and Peng, X.F. (2015) Exact Solutions of Non-Linear Fractional Partial Differential Equations by Fractional Sub-Equation Method. Thermal Science, 19, 1239-1244. https://doi.org/10.2298/TSCI1504239M
|
[15]
|
Mohyud-Din, S.T., Nawaz, T., Azhar, E. and Akbar, M.A. (2015) Fractional Sub-Equation Method to Space-Time Fractional Calogero-Degasperis and Potential Kadomtsev-Petviashvili Equations. Journal of Taibah University for Science, 11, 258-263.
|
[16]
|
Nino, U.F., Leal, H.V., Khan, Y., Díaz, D.P., Sesma, A.P., Fernández, V.J. and Orea, J.S. (2014) Modiffed Nonlinearities Distribution Homotopy Perturbation Method as a Tool to FFND Power Series Solutions to Ordinary Differential Equations. Springerplus, 3, 1-13.
|
[17]
|
Cuce, E. and Cuce, P.M. (2015) A Successful Application of Homotopy Perturbation Method for Efficiency and Effectiveness Assessment of Longitudinal Porous FFNS. Energy Conversion and Management, 93, 92-99.
https://doi.org/10.1016/j.enconman.2015.01.003
|
[18]
|
Sayevand, K. and Jafari, H. (2016) On Systems of Nonlinear Equations: Some Modified Iteration Formulas by the Homotopy Perturbation Method with Accelerated Fourth-And FFFTH-Order Convergence. Applied Mathematical Modelling, 40, 1467-1476. https://doi.org/10.1016/j.apm.2015.06.030
|
[19]
|
Xu, H., Liao, S.J. and You, X.C. (2009) Analysis of Nonlinear Fractional Partial Differential Equations with the Homotopy Analysis Method. Communications in Nonlinear Science and Numerical Simulation, 14, 1152-1156.
https://doi.org/10.1016/j.cnsns.2008.04.008
|
[20]
|
Jafari, H. and Seiff, S. (2009) Homotopy Analysis Method for Solving Linear and Nonlinear Fractional Diffusion- Wave Equation. Communications in Nonlinear Science and Numerical Simulation, 14, 2006-2012.
https://doi.org/10.1016/j.cnsns.2008.05.008
|
[21]
|
Jafari, H. and Seiff, S. (2009) Solving a System of Nonlinear Fractional Partial Differential Equations Using Homotopy Analysis Method. Communications in Nonlinear Science and Numerical Simulation, 14, 1962-1969.
https://doi.org/10.1016/j.cnsns.2008.06.019
|
[22]
|
Luchko, Y. and Gorenflo, R. (1999) An Operational Method for Solving Fractional Differential Equations with the Caputo Derivatives. Acta Mathematica Vietnamica, 24, 207-233.
|
[23]
|
Moustafa, O.L. (2003) On the Cauchy Problem for Some Fractional Order Partial Differential Equations. Chaos, Solitons & Fractals, 18, 135-140. https://doi.org/10.1016/S0960-0779(02)00586-6
|
[24]
|
Pandey, R.K. and Mishra, H.K. (2016) Homotopy Analysis Fractional Sumudu Transform Method for Time Fractional Third Order Dispersive Partial Differential Equation. Advances in Computational Mathematics, 43, 365-383.
|
[25]
|
Oldham, K.B. and Spanier, J. (1974) The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. Academic Press, New York and London.
|
[26]
|
Belgacem, F.B.M. and Karaballi, A.A. (2006) Sumudu Transform Fundamental Properties Investigations and Applications. Journal of Applied Mathematics and Stochastic Analysis, 2006, 1-23.
https://doi.org/10.1155/JAMSA/2006/91083
|
[27]
|
HE. J.H. (2014) A Tutorial Review on Fractal Space Time and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718. https://link.springer.com/article/10.1007/s10773-014-2123-8
|
[28]
|
Kilbas, A.A., Saigo, M. and Saxena, R.K. (2004) Generalized Mittag-Leffler Function and Generalized Fractional Calculus Operators. Integral Transforms and Special Functions, 15, 31-49.
https://doi.org/10.1080/10652460310001600717
|
[29]
|
Morales-Delgado1, V.F., Gómez-Aguilar, J.F., Yépez-Martínez, H., Baleanu, D., Escobar-Jimenez, R.F. and Olivares- Pregrino, V.H. (2016) Laplace Homotopy Analysis Method for Solving Linear Partial Differential Equations Using a Fractional Derivative with and without Kernel Singular. Advances in Difference Equations, 164, 1-17.
https://doi.org/10.1186/s13662-016-0891-6
|