Electron. J. Differential Equations

Electron. J. Differential Equations, Vol. 2024 (2024), No. 36, pp. 1-9.

Existence of pseudosolutions for dynamic fractional differential equations
Aneta Sikorska-Nowak

Abstract:
In this article, we consider the existence of pseudosolutions for boundary value problem for fractional differential equations of the form

\begin{matrix} _{T}^{C} Δ^{α} x (t) = f (t, x (t)), for t \in I_{a} = [0, a] \cap T, \\ x (0) = x_{0}, x_{0} \in E, \end{matrix}

where

_{T}^{C} Δ^{α} x (t)

α \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

	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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Existence of pseudosolutions for dynamic fractional differential equations Aneta Sikorska-Nowak

Existence of pseudosolutions for dynamic fractional differential equations
Aneta Sikorska-Nowak