1,575
Views
64
CrossRef citations to date
0
Altmetric
Original Article

Numerical computation of fractional Black–Scholes equation arising in financial marketFootnote

, &
Pages 177-183 | Received 24 Dec 2013, Accepted 27 Oct 2014, Published online: 14 Mar 2019

References

  • F.BlackM.S.ScholesThe pricing of options and corporate liabilitiesJ Polit Econ811973637654
  • J.M.ManaleF.M.MahomedA simple formula for valuing American and European call and put optionsJ.BanasiakProceeding of the Hanno Rund workshop on the differential equations2000University of Natal210220
  • R.K.GazizovN.H.IbragimovLie symmetry analysis of differential equations in financeNonlinear Dynam171998387407
  • M.BohnerY.ZhengOn analytical solution of the Black-Scholes equationAppl Math Lett222009309313
  • R.CompanyE.NavarroJ.R.PintosE.PonsodaNumerical solution of linear and nonlinear Black-Scholes option pricing equationsComput Math Appl562008813821
  • Z.CenA.LeA robust and accurate finite difference method for a generalized Black Scholes equationJ Comput Appl Math235201137283733
  • R.CompanyL.JódarJ.R.PintosA numerical method for European option pricing with transaction costs nonlinear equationMath Comput Model502009910920
  • F.FabiaoM.R.GrossinhoO.A.SimoesPositive solutions of a Dirichlet problem for a stationary nonlinear Black Scholes equationNonlinear Anal71200946244631
  • P.AmsterC.G.AverbujM.C.MarianiSolutions to a stationary nonlinear Black–Scholes type equationJ Math Anal Appl2762002231238
  • P.AmsterC.G.AverbujM.C.MarianiStationary solutions for two nonlinear Black–Scholes type equationsAppl Numer Math472003275280
  • J.AnkudinovaM.EhrhardtOn the numerical solution of nonlinear Black–Scholes equationsComput Math Appl562008799812
  • V.GülkaçThe homotopy perturbation method for the Black-Scholes equationJ Stat Comput Simul80201013491354
  • K.B.OldhamJ.SpanierThe fractional calculus1974Academic PressNew York
  • K.S.MillerB.RossAn introduction to the fractional calculus and fractional differential equations2003Johan Willey and Sons, Inc.New York
  • I.PodlubnyFractional differential equations calculus1999Academic, PressNew, York
  • A.A.KilbasH.M.SrivastavaJ.J.TrujilloTheory and applications of fractional differential equations2006ElsevierAmsterdam
  • I.PodlubnyGeometric and physical interpretation of fractional integration and fractional differentiationFract Calc Appl Anal52002367386
  • J.H.HeHomotopy perturbation techniqueComput Methods Appl Mech Engrg1781999257262
  • J.H.HeApplication of homotopy perturbation method to nonlinear wave equationsChaos Solitons Fractals262005695700
  • J.H.HeA coupling method of homotopy technique and perturbation technique for nonlinear problemsInt J Nonlinear Mech3520003743
  • J.H.HeSome asymptotic methods for strongly nonlinear equationsInter J Mod Phys B20200611411199
  • J.H.HeA new perturbation technique which is also valid for large parametersJ Sound Vibration229200012571263
  • A.YildirimH.KocakHomotopy perturbation method for solving the space–time fractional advection-dispersion equationAdv Water Resour32200917111716
  • A.YildirimY.GulkanatAnalytical approach to fractional Zakharov–Kuznetsov equations by He's homotopy perturbation methodCommun Theor Phys5320101005
  • O.AbdulazizI.HasimE.S.IsmailApproximate analytical solution to fractional modified KdV equationsMath Comput Model492009136145
  • N.A.KhanA.AraA.MahmoodApproximate solution of time fractional chemical engineering equation: a comparative studyInt J Chem Rect Eng82010A 19
  • S.J.LiaoBeyond perturbation: introduction to homotopy analysis method2003Chapman and Hall/CRC PressBoca Raton
  • S.J.LiaoOn the homotopy analysis method for nonlinear problemsAppl Math Comput1472004499513
  • S.J.LiaoA new branch of solutions of boundary-layer flows over an impermeable stretched plateInt J Heat Mass Transf48200525292539
  • S.J.LiaoAn approximate solution technique not depending on small parameters: a special exampleInt J Non Linear Mech3031995371380
  • S.J.LiaoA new branch of solutions of boundary-layer flows over an impermeable stretched planeInt J Heat Mass Transf4812200525292539
  • T.HayatM.KhanM.AyubOn the explicit solutions of an Oldroyd 6-constant fluidInt J Eng Sci422004125135
  • T.HayatM.KhanHomotopy solution for generalized second-grade fluid fast porous plateNonlinear Dyn422005395405
  • A.ShidfarA.MolabahramiA weighted algorithm based on the homotopy analysis method: application to inverse heat conduction problemsCommun Nonlinear Sci Num Simul15201029082915
  • H.KheiriN.AlipourR.DehganiHomotopy analysis and Homotopy-Pade methods for the modified Burgers-Korteweg-de-Vries and the Newell Whitehead equationMath Sci5120113350
  • M.CaputoElasticita e Dissipazione1969Zani-ChelliBologna
  • G.M.Mittag-LefflerSur la nouvelle fonction Eα(x)CR Acad Sci Paris (Ser.II)1371903554558