Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland
email: anetas@amu.edu.pl
Aneta Sikorska-Nowak
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.
DOI: 10.58997/ejde.2024.36
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Aneta Sikorska-Nowak Faculty of Mathematics and Computer Science Adam Mickiewicz University Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland email: anetas@amu.edu.pl |
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