On a class of fractional differential equations in a Sobolev space

Abstract

This article is concerned with the study of the existence and uniqueness of solutions to a class of fractional differential equations in a Sobolev space. The fractional time derivative is considered in Riemann–Liouville sense. An application to a fractional diffusion equation in a bounded domain with null Dirichlet boundary conditions is given.

Keywords:

• fractional differential equation
• m-dissipatif operator
• Sobolev space
• Dirichlet boundary conditions

AMS Subject Classifications::

• 49J20
• 49K20
• 34K05
• 34A12
• 26A33