Sayed Khalil M. Elagan

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A partial group as defined in [3] is a semigroup S which satisfies the following axioms. (i) For every x ∈ S, there exists a (necessarily unique) element ex ∈ S, called the partial identity of x such that exx =xex =x and if yx =xy =x then ex y = yex = ex. (ii) For every x ∈ S, there exists a (necessarily unique) element x−1 ∈ S, called the partial inverse(More)
A q partial group is defined to be a partial group, that is, a strong semilattice of groups S= [E(S);Se,φe, f ] such that S has an identity 1 and φ1,e is an epimorphism for all e ∈ E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1 = S1. This Q operation is proved to commute with Cartesian products and(More)
In this paper, we applied a new analytical geometrical method which so called fractal index method to find a new solution of the generalized fractional Riccati equation of arbitrary order, we also wrote the solution on the closed form as an infinte series and showed that the series is convergent within some closed disk. The fractional operators are taken in(More)
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