Strict Hölder regularity for fractional order abstract degenerate differential equations

Novel interpolation spaces and maximal‐weighted Hölder regularity results for the fractional abstract Cauchy problem

“…Also, Alam et al. [2, 3] looked into the strict Hölder regularity for the fractional abstract Cauchy problem and degenerate problem in the space $$C^{\alpha }(X)$$, respectively, by constructing the interpolation spaces in terms of resolvent families. It is worth mentioning that the resolvent family theory is a primary extension of the operator semigroup theory.…”

“…Moreover, the author was devoted to presenting the maximal regularity for various types of integer-order Cauchy problems in terms of interpolation spaces. Also, Alam et al [2,3] looked into the strict Hölder regularity for the fractional abstract Cauchy problem and degenerate problem in the space 𝐶 𝛼 (𝑋), respectively, by constructing the interpolation spaces in terms of resolvent families. It is worth mentioning that the resolvent family theory is a primary extension of the operator semigroup theory.…”