On well-posed solvability of boundary value problems for equations with fractional derivatives in hyper-weight spaces of continuous functions on

Abstract

In the paper, we establish uniformly well-posed solvability of boundary value problems for equations , in the Banach space where the operator A is a generator of semi-group U(x) of the class with the estimate , , M does not depend on x. The results are applied to the investigation of well-posed solvability of boundary value problems for differential equations with fractional derivatives in weight spaces of continuous functions and investigation of problems of heat-and-mass-transfer and of radio physics.

Keywords:

• Well-posed problems
• strongly continuous semi-groups of operators
• fractional degrees of operators
• fractional derivatives
• fractional integrals
• alarm problem

AMS Subject Classifications:

• 26A33
• 34K37
• 47D03
• 47D06

Notes

No potential conflict of interest was reported by the author.