Geodesic
Nonlinear system of impulsive integro-differential equations with Hilfer fractional operator and mixed maxima
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 3, pp. 312-325

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A nonlocal boundary value problem for a system of ordinary integro-differential equations with impulsive effects, nonlinear mixed maxima and fractional order Hilfer operator is investigated. The nonlinear boundary value condition is given in the nonlinear integral form. The problem is reduced to the nonlinear system of functional integral equations. The system of functional integral equations has terms of nonlinear functions in integral and non-integral forms. The method of successive approximations in a combination with the method of compressing mapping is used in proving the unique solvability of the boundary value problem.
Keywords: impulsive integro-differential equation, Hilfer fractional operator, nonlocal boundary condition, mixed maxima, unique solvability. 
@article{CHFMJ_2022_7_3_a4,
     author = {T. K. Yuldashev and T. G. Ergashev and T. A. Abduvahobov},
     title = {Nonlinear system of impulsive integro-differential equations with {Hilfer} fractional operator and mixed maxima},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {312--325},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_3_a4/}
}
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T. K. Yuldashev; T. G. Ergashev; T. A. Abduvahobov. Nonlinear system of impulsive integro-differential equations with Hilfer fractional operator and mixed maxima. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 3, pp. 312-325. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_3_a4/