On the dimension of the solution set for semilinear fractional differential inclusions
Summary: The main tools of our study include some well-known results on multivalued maps. We study the following problem for semilinear fractional differential inclusion with nonlocal condition: \[ ^cD^qx(t)\in A(t)x(t)+F(t,x(t)),\;t\in[0,T](T>0),\quad x(0)+g(x)=x_0,\;x_0\in \mathbb{R}^n, \] where \(^cD_q\) denote the Caputo fractional derivative of order \(q\in(0,1]\), \(A(t)\)is a bounded linear operator on \(0,T]\) (the function \(t\to A(t)\) is continuous in the uniform operator topology), \(g:{\mathcal C}([0,T],\mathbb{R}^n)\to\mathbb{R}^n\), and \(F:[0,T]\times\mathbb{R}^n\to P(\mathbb{R}^n)\), where \(P(\mathbb{R}^n)\) is the family of all nonempty subsets of \(\mathbb{R}^n\).
scientific article; zbMATH DE number 6058102
scientific article