This study addresses a novel identification of Adomian Decomposition Method (ADM) to have an accurate and quick solution for the European option pricing problem by using BlackScholes equation of timefractional order (FBSE) with the initial condition and generalized BlackScholes equation of fractional order (GFBSE). The fractional operator is understood in the Caputo mean. First of all, we redefine the BlackScholes equation as fractional mean which computes the option price for fractional values. Then we have applied the ADM to the FBSE and GFBSE, so we have obtained accurate and quick approximate analytical solutions for these equations. The results related to the solutions have been presented in figures.
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Bibtex  @araştırma makalesi { konuralpjournalmath359520,
journal = {Konuralp Journal of Mathematics (KJM)},
issn = {},
eissn = {2147625X},
address = {Mehmet Zeki SARIKAYA},
year = {2018},
volume = {6},
pages = {102  109},
doi = {},
title = {A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series},
key = {cite},
author = {Yavuz, Mehmet and Özdemir, Necati}
} 
APA  Yavuz, M , Özdemir, N . (2018). A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series. Konuralp Journal of Mathematics (KJM), 6 (1), 102109. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/359520 
MLA  Yavuz, M , Özdemir, N . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 (2018): 102109 <http://dergipark.gov.tr/konuralpjournalmath/issue/31478/359520> 
Chicago  Yavuz, M , Özdemir, N . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 (2018): 102109 
RIS  TY  JOUR T1  A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series AU  Mehmet Yavuz , Necati Özdemir Y1  2018 PY  2018 N1  DO  T2  Konuralp Journal of Mathematics (KJM) JF  Journal JO  JOR SP  102 EP  109 VL  6 IS  1 SN  2147625X M3  UR  Y2  2017 ER  
EndNote  %0 Konuralp Journal of Mathematics A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series %A Mehmet Yavuz , Necati Özdemir %T A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series %D 2018 %J Konuralp Journal of Mathematics (KJM) %P 2147625X %V 6 %N 1 %R %U 
ISNAD  Yavuz, Mehmet , Özdemir, Necati . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 / 1 (Nisan 2018): 102109. 