In this paper, an analog of the conformable fractional derivative is defined in arbitrary finite-dimensional commutative associative algebra. Functions taking values indicated algebras and having derivatives sense a are called φ-monogenic. A relation between concepts φ-monogenic monogenic functions such has been established. Two new definitions have proposed for with algebras.

There is a debate among contemporary mathematicians about what it really means by a fractional derivative. The question arose as a consequence of introducing a ‘new’ definition of a fractional derivative. In a reply Ortigueira and Machado [1] came up with several very important criteria to determine whether a given derivative is a fractional derivative. According to their criterion, the new fra...

In this study, we study the oscillatory solutions of conformable fractional differential equations with damping term. Some examples have been given to illustrate results.