Geodesic
The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
Filomat, Tome 37 (2023) no. 12, p. 3871

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DOI

In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα∗ u(t) = f (t,u(t),u ′(t), CDβu(t)), 0 t 1, 1 α 2, 0 β ⩽ 1, u(0) = A, u(1) = Bu(η), where 0 η 1, A ⩾ 0, Bη > 1, Dα∗ is the modified Caputo fractional derivative of order α, CDβ is the Caputo fractional derivative of order β, and f is a function in C([0, 1] ×R ×R ×R). Existence results for a solution are obtained. Two examples are presented to illustrate the results.
DOI : 10.2298/FIL2312871A
Classification : 34A08, 26A33, 34B99
Keywords: Fractional Differential Equations, Green’s Functions, Boundary Value Problem 
Suzana Aleksić; Alberto Cabada; Slađana Dimitrijević; Tatjana V Tomović Mladenović. The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function. Filomat, Tome 37 (2023) no. 12, p. 3871 . doi: 10.2298/FIL2312871A
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     title = {The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function},
     journal = {Filomat},
     pages = {3871 },
     year = {2023},
     volume = {37},
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     doi = {10.2298/FIL2312871A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312871A/}
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