Abstract
this paper devoted to study the existence of a unique solution of
the fractional Hammerstein integro-differential equations in the Banach space via the fixed
point theorems. The main purpose is based on transforming the fractional equations into
the integral equations of the Volterra type by using the differential transformation method
and the corresponding fractional calculus characteristics. Also, we obtain the ε-modified
operational matrix for the fractional integral and use the properties of modified block pulse
functions to get approximate solutions. In the our presented method, the fractional Hammerstein equations are transformed into a system of algebraic equations, where the volume
of computations are reduced by using the special nodes. Finally, we give some examples
to demonstrate the obtained results.
Somayyeh Dadsetadi, Kazem Nouri. (2020) Analytical and Numerical Investigation of the Hammerstein Fractional Equations, Punjab University Journal of Mathematics, Volume 52 , Issue No.1.
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