A global existence and uniqueness theorem in the extended sense for ordinary differential equations of fractional order

الملخص EN

This research proves a global existence and uniqueness theorem by using the Banach contraction principle for the following initial-value problem : g() (x) =  (x, g (x)) almost all x  I.

With g(a-1) () = b  ().

0<≤1.

Where I is any compact interval in the real line R containing the point  .

g() is the derivative of order  of a real-valued function g.

 () is the Gamma function and b is a real number.

assuming weaker conditions (known as the Caratheodory conditions) on the function .