Non-uniqueness of solution for initial value problem of impulsive fractional partial differential equations

Zhang, Xian Min

doi:10.1504/ijdsde.2022.10051397

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2024

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“…Moreover, by combining the above two thoughts of equivalent integral equation, the third equivalent integral equation of (1.1) was given in [51].…”

Section: Introductionmentioning

confidence: 99%

Impulsive fractional partial differential system and its correct equivalent integral equation

Zhang,

Liu,

Peng

et al. 2024

Math Methods in App Sciences

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It is found that there are two piecewise functions to satisfy the conditions in the impulsive fractional partial differential system (IFrPDS), which deduce that the three different equivalent integral equations of the IFrPDS given in the cited papers are inappropriate. Next, by applying two limit properties of the IFrPDS and the properties of piecewise function, the new formula of equivalent integral equation of the IFrPDS is discovered that is the integral equation with an arbitrary continuously differentiable function of on to reveal the non‐uniqueness of the IFrPDE's solution. Finally, an example is provided to expound the computation of the equivalent integral equation of the IFrPDS.

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“…Moreover, by combining the above two thoughts of equivalent integral equation, the third equivalent integral equation of (1.1) was given in [51].…”

Section: Introductionmentioning

confidence: 99%

Impulsive fractional partial differential system and its correct equivalent integral equation

Zhang,

Liu,

Peng

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Non-uniqueness of solution for initial value problem of impulsive fractional partial differential equations

Cited by 1 publication

References 0 publications

Impulsive fractional partial differential system and its correct equivalent integral equation

Impulsive fractional partial differential system and its correct equivalent integral equation

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