Semilinear Conformable Fractional Differential Equations in Banach Spaces
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We introduce the concept of a mild solution of conformable fractional abstract initial value problem. We establish the existence and uniqueness theorem using the contraction principle. As a regularity result for a linear problem, we show that the mild solution is in fact a strong solution. We give an example to demonstrate the applicability of the established theoretical results.
KeywordsConformable fractional derivative Fractional-order differential equation Banach fixed point theorem
Mathematics Subject ClassificationMSC 34G10 MSC 34G20
The authors would like to thanks the referees for their valuable comments and suggestions which have considerably improved our original manuscript.
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