| Citation: |
Palidan Wusiman, Haibo Gu. INTERVAL-VALUED FRACTIONAL DIFFERENTIAL EQUATIONS WITH LENGTH CONSTRAINTS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2079-2096. doi: 10.11948/20250125
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INTERVAL-VALUED FRACTIONAL DIFFERENTIAL EQUATIONS WITH LENGTH CONSTRAINTS
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Abstract
This article investigates the existence of solutions for Caputo-type interval-valued fractional differential equations (IVFDEs) with length constraints. We begin by considering a class of IVFDEs that include impulsive effects. Then, we explore IVFDEs with impulses related to length constraints. Using fixed-point theory, we obtain several existence results. Importantly, we employ impulses to control the length of solutions to IVFDEs. Additionally, we present several examples to demonstrate our main results.
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References
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Palidan Wusiman, Haibo Gu. INTERVAL-VALUED FRACTIONAL DIFFERENTIAL EQUATIONS WITH LENGTH CONSTRAINTS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2079-2096. doi: 10.11948/20250125
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Figure 1.
Graph of the forward solution (3.9) (the red curve represents
$ \underline \varphi(\zeta) $ $ \overline \varphi(\zeta) $ -
Figure 2.
Graph of the forward solution (3.11) (the red curve represents
$ \underline \varphi(\zeta) $ $ \overline \varphi(\zeta) $ -
Figure 3.
The forward solution to problem (4.4) with
$ A>25 $ $ \underline \varphi(\zeta) $ $ \overline \varphi(\zeta) $ $ len(\varphi(\zeta)) $ -
Figure 4.
The forward solution to problem (4.4) with
$ A=10 $ $ \underline \varphi(\zeta) $ $ \overline \varphi(\zeta) $ $ len(\varphi(\zeta)) $