Existence of pseudosolutions for dynamic fractional differential equations

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.  For more information see https://ejde.math.txstate.edu/Volumes/2024/36/abstr.html