Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 36, pp. 1-9.

Title: Existence of pseudosolutions for dynamic fractional differential equations

Author: Aneta Sikorska-Nowak (Adam Mickiewicz Univ., Poland)

Abstract: 
In this article, we consider the existence of pseudosolutions for boundary value 
problem for fractional differential equations of the form
$$\displaylines{
{}_T^C \Delta ^ \alpha x(t)=f(t,x(t)), \quad \hbox{for } t \in I_a=[0,a] \cap T, \cr
x(0)=x_0,\quad  x_0 \in E,
}$$
where \({}_T^C \Delta ^ \alpha x(t)\), \(\alpha \in (0,1]\) denotes the Caputo fractional 
derivative, \(T\) denotes a time scale, and the function \(f\) is weakly-weakly 
sequentially continuous with values in a Banach space \(E\) and satisfies some 
boundary conditions and conditions expressed in terms of measures of weak 
non-compactness.

Submitted  May 20, 2024. Published June 20, 2024.
Math Subject Classifications: 34K40, 34K42, 34A08, 34G20.
Key Words: Fractional differential equations; fixed point; time scales; Caputo fractional derivative;  delta HKP integral.