Existence and uniqueness of mild solutions for conformable fractional differential equations using new generalized conformable fractional derivative and semigroup

Key Points

• The aim is to generalize the conformable derivative and study mild solutions in fractional differential equations.
• Generalization of the conformable derivative.
• Introduction of conformable strongly continuous semigroup and its generator.
• Analysis of mild solutions for the proposed semigroup.
• Establishment of existence and uniqueness of mild solutions.
• Demonstration of continuous dependence of mild solutions on initial data.