Geodesic
Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative
Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 4, pp. 418-424

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In this paper, we prove the unique solvability of an analogue problem Darboux for a loaded integro-differential equation with Caputo operator by method of integral equations. The problem is equivalently reduced to a system of integral equations, which is unconditionally and uniquely solvable.
Keywords: integro-differential equations, Caputo fractional derivative, loaded equation, nonlocal problem, Bessel function. 
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     author = {U. Baltaeva and Y. Alikulov and I. I. Baltaeva and A. Ashirova},
     title = {Analog of the {Darboux} problem for a loaded integro-differential equation involving the {Caputo} fractional derivative},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {418--424},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2021_12_4_a1/}
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U. Baltaeva; Y. Alikulov; I. I. Baltaeva; A. Ashirova. Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative. Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 4, pp. 418-424. http://geodesic.mathdoc.fr/item/NANO_2021_12_4_a1/