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In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

The fractional Black–Scholes pricing model widely appears in financial markets. This paper presents the special class of operational matrix to approximate the solution of fractional Black–Scholes equation based on the Boubaker polynomial functions. The Boubaker operational matrix of the fractional derivative converts the model to obtain the numerical solution of the time‐fractional Black–Scholes equation. The numerical results are displayed in some tables for better illustration with testing in some examples.

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In this paper we may use piece wise constant functions for the special type of system of second kind integro differential equation of the first order. The main problem is reduced to linear system of algebraic equations. Some numerical examples are dedicated for showing efficiency and validity of the method.