in this paper, a new identification of the lagrange multipliers by means of the sumudu transform, is employed to  btain a quick and accurate solution to the fractional black-scholes equation with the initial condition for a european option pricing problem. undoubtedly this model is the most well known model for pricing financial derivatives. the fractional derivatives is described in caputo sen...

In the paper, we first define a degenerate Pochhammer symbol by using gamma function and investigate its properties. By symbol, introduce hypergeometric function. We also Sumudu transform properties exponential Finally, give certain integral representations, derivative formulas, transforms, factional calculus applications, generating functions of

and Applied Analysis 3 For each complex number x,ΨP x define a linear mapping of C|N| into C. If anyNj is zero, Ψ i,j P is the empty matrix for all i and the corresponding column of matrices in ΨP is absent. If Nj 0 for all j,ΨP x is defined to be the unique linear mapping of {0} C0 into C; its matrix representation is then the empty matrix. In particular consider ΨP x ( x4 2x2 1 − 2x 3x4 2x 4x3 )

This research work is dedicated to solving the n-generalized Korteweg–de Vries (KdV) equation in a fractional sense. The method combination of Sumudu transform and Adomian decomposition method. has significant advantages for differential equations that are both linear nonlinear. It easy find solutions fractional-order PDEs with less computing labor.