Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation methodFootnote

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References

• K.AbbaouiY.CherruaultNew ideas for proving convergence of decomposition methodsComput. Math. Appl.291995103108
   Web of Science ®Google Scholar
• M.AkbarzadeJ.LangariApplication of homotopy perturbation method and variational iteration method to three dimensional diffusion problemInt. J. Math. Anal.5182011871880
   Google Scholar
• M.A.AsiruSumudu transform and the solution of integral equation of convolution typeInt. J. Math. Educ. Sci. Technol.322001906910
   Google Scholar
• A.AtanganaD.BaleanuNonlinear fractional Jaulent–Miodek and Whitham–Broer–Kaup equations within sumudu transformAbstract Appl. Anal.2013 Article ID 160681, 8 pages
   Google Scholar
• A.AtanganaA.KilicmanThe use of sumudu transform for solving certain nonlinear fractional heat-like equationsAbs. Appl. Anal.2013 Article ID 737481, 12 pages
   Google Scholar
• A.AtanganaA.SecerThe time-fractional coupled-Korteweg-de-vries equationsAbst. Appl. Anal.2013 Article ID 947986, 8 pages
   Google Scholar
• F.B.M.BelgacemA.A.KaraballiSumudu transform fundamental properties investigations and applicationsJ. Appl. Math. Stochastic Anal.2006 Article ID 91083, 23 pages
   Google Scholar
• F.B.M.BelgacemA.A.KaraballiS.L.KallaAnalytical investigations of the sumudu transform and applications to integral production equationsMath. Prob. Eng.32003103118
   Google Scholar
• M.CaputoElasticita e Dissipazione1969Zani-ChelliBologna
   Google Scholar
• V.B.L.ChaurasiaJ.SinghApplication of sumudu transform in Schrödinger equation occurring in quantum mechanicsAppl. Math. Sci.47201028432850
   Google Scholar
• L.DebnathFractional integrals and fractional differential equations in fluid mechanicsFrac. Calc. Appl. Anal.62003119155
   Google Scholar
• D.D.GanjiThe applications of He’s homotopy perturbation method to nonlinear equation arising in heat transferPhys. Lett. A3352006337341
   Google Scholar
• Z.Z.GanjiD.D.GanjiA.GanjiM.RostamianAnalytical solution of time-fractional Navier-Stokes equation in polar coordinate by homotopy perturbation methodNum. Meth. Part. Diff. Equat.2642010117124
   Google Scholar
• A.GhorbaniBeyond adomian’s polynomials: He polynomialsChaos, Solitons Fractals39200914861492
   Web of Science ®Google Scholar
• M.A.GondalM.KhanHomotopy perturbation method for nonlinear exponential boundary layer equation using Laplace transformation, He’s polynomials and Pade technologyInt. J. Non. Sci. Numer. Simul.11201011451153
   Google Scholar
• J.H.HeHomotopy perturbation techniqueComput. Methods Appl. Mech. Eng.1781999257262
   Web of Science ®Google Scholar
• J.H.HeHomotopy perturbation method: a new nonlinear analytical techniqueAppl. Math. Comput.13520037379
   Web of Science ®Google Scholar
• J.H.HeNew interpretation of homotopy perturbation methodInt. J. Mod. Phys. B20200625612568
   Web of Science ®Google Scholar
• R.HilferApplications of Fractional Calculus in Physics2000World Scientific Publishing CompanySingapore-New Jersey-Hong Kong 87–130
   Google Scholar
• H.JafariM.ZabihiM.SaidyApplication of homotopy perturbation method for solving gas dynamics equationAppl. Math. Sci.248200823932396
   Google Scholar
• M.KhanM.HussainApplication of Laplace decomposition method on semi-infinite domainNum. Algorithms562011211218
   Google Scholar
• M.KhanM.A.GondalS.KumarA new analytical solution procedure for nonlinear integral equationsMath. Comp. Model.55201218921897
   Google Scholar
• S.A.KhuriA Laplace decomposition algorithm applied to a class of nonlinear differential equationsJ. Appl. Math.12001141155
   Google Scholar
• A.A.KilbasH.M.SrivastavaJ.J.TrujilloTheory and Applications of Fractional Differential Equations2006ElsevierAmsterdam
   Google Scholar
• S.KumarO.P.SinghNumerical inversion of the abel integral equation using homotopy perturbation methodZeitschrift fur Naturforschung65a2010677682
   Google Scholar
• S.KumarH.KocakA.YildirimA fractional model of gas dynamics equation by using Laplace transformZeitschrift fur Naturforschung67a2012389396
   Google Scholar
• F.MainardiY.LuchkoG.PagniniThe fundamental solution of the space-time fractional diffusion equationFract. Calculus Appl. Anal.42001153192
   Google Scholar
• K.S.MillerB.RossAn Introduction to the Fractional Calculus and Fractional Differential Equations1993WileyNew York
   Google Scholar
• S.T.Mohyud-DinM.A.NoorK.I.NoorTraveling wave solutions of seventh-order generalized KdV equation using He’s polynomialsInt. J. Nonlinear Sci. Num. Simulat.102009227233
   Web of Science ®Google Scholar
• K.B.OldhamJ.SpanierThe Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order1974Academic PressNew York
   Google Scholar
• I.PodlubnyFractional Differential Equations1999Academic PressNew York
   Google Scholar
• M.M.RashidiD.D.GanjiHomotopy Perturbation Combined with Pad́e Approximation for Solving Two Dimensional Viscous Flow in the Extrusion ProcessInt. J. Nonlinear Sci.742009387394
   Google Scholar
• M.M.RashidiD.D.GanjiS.DinarvandExplicit analytical solutions of the generalized Burger and Burger-Fisher equations by homotopy perturbation methodNum. Meth.2522009409417
   Google Scholar
• M.SiddiqueNumerical computation of two-dimensional diffusion equations with non local boundary conditionsIAENG Int. J. Appl. Math.4012010 JAM_40_1_04
   Google Scholar
• J.SinghD.KumarSushilaHomotopy perturbation sumudu transform method for nonlinear equationsAdv. Theor. Appl. Mech.42011165175
   Google Scholar
• J.SinghD.KumarA.KilicmanHomotopy perturbation method for fractional gas dynamics equation using sumudu transformAbst. Appl. Anal.2013 Article ID 934060, 8 pages
   Google Scholar
• SushilaJagdevSinghY.S.ShihodiaAn efficient analytical approach for MHD viscous flow over a stretching sheet via homotopy perturbation sumudu transform methodAin Shams Eng. J.42013549555
   Google Scholar
• G.K.WatugalaSumudu transform- a new integral transform to solve differential equations and control engineering problemsInt. J. Math. Edu. Sci. Technol.24119933543
   Google Scholar
• A.YildirimAn algorithm for solving the fractional nonlinear Schröndinger equation by means of the homotopy perturbation methodInt. J. Nonlinear Sci. Num. Simulat.102009445451
   Web of Science ®Google Scholar
• G.O.YoungDefinition of physical consistent damping laws with fractional derivativesZ. Angew. Math. Mech.751995623635
   Google Scholar