Geodesic
Fractional differential equations with maxima on time scale via Picard operators
Filomat, Tome 37 (2023) no. 2, p. 393

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DOI

In this paper, we prove a result of existence and uniqueness of solutions for the following class of problem of initial value for differential equations with maxima and Caputo's fractional order on the time scales: c ∆ ω a u(ϑ) = ζ(ϑ, u(ϑ), max ς∈[a,ϑ] u(ς)), ϑ ∈ J := [a, b] T , 0 ω ≤ 1, u(a) = ϕ, We used the techniques of the Picard and weakly Picard operators to obtain some data dependency on the parameters results.
DOI : 10.2298/FIL2302393K
Classification : 7H10, 54H25
Keywords: Fractional differential equations, Existence, Time scale, Picard operator, Initial value problem, Maxima, Fixed point, Abstract comparison principle, Data dependance 
Erdal Karapınar; Nadia Benkhettou; Jamal Eddine Lazreg; Mouffak Benchohra. Fractional differential equations with maxima on time scale via Picard operators. Filomat, Tome 37 (2023) no. 2, p. 393 . doi: 10.2298/FIL2302393K
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     title = {Fractional differential equations with maxima on time scale via {Picard} operators},
     journal = {Filomat},
     pages = {393 },
     year = {2023},
     volume = {37},
     number = {2},
     doi = {10.2298/FIL2302393K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2302393K/}
}
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