Non-instantaneous impulsive fractional integro-differential equations with proportional fractional derivatives with respect to another function
DOI:
https://doi.org/10.24193/subbmath.2023.3.07Keywords:
Non-instantaneous impulses, Proportional fractional derivatives, Leray-Schauder alternativeAbstract
This paper concerns the existence and uniqueness of solutions of non-instantaneous impulsive fractional integro-differential equations with proportional fractional derivatives with respect to another function.By the aid of the nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicabilityof the theoretical results.
References
Abbas, M.I., emph{On the initial value problems for the Caputo-Fabrizio impulsive fractional differential equations}, Asian-Eur. J. Math., (2021), 2150073, DOI: 10.1142/S179355712150073X.
Abbas, M.I., emph{Ulam stability of fractional impulsive differential equations with Riemann-Liouville integral boundary conditions}, J. Contemp. Math. Anal., textbf{50}(5)(2015), 209-219.
Agarwal, R., Hristova, S., O'Regan, D., emph{Iterative techniques for the initial value problem for Caputo fractional differential equations with non-instantaneous impulses}, Appl. Math. Comput., textbf{334}(2018), 407-421.
Anderson, D.R., Ulness, D.J., emph{Newly defined conformable derivatives}, Adv. Dyn. Syst. Appl., {bf10}(2)(2015), 109-137.
Dugundji, J., Granas, A., emph{Fixed Point Theory}, Warsaw, 1982.
Hern'{a}ndaz, E., O'Regan, D., emph{On a new class of abstract impulsive differential equation},
Proc. Amer. Math. Soc., textbf{141}(2013), 1641-1649.
Jarad, F., Abdeljawad, T., Rashid, S., Hammouch, Z.,
emph{More properties of the proportional fractional integrals and derivatives of a
function with respect to another function},
Adv. Differential Equations, (2020), 2020:303.
Jarad, F., Alqudah, M.A., Abdeljawad, T.,
emph{On more general forms of proportional fractional operators},
Open Math., textbf{18}(2020), 167-176.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.,
emph{A new definition of fractional derivative},
J. Comput. Appl. Math., {bf264}(2014), 65-70.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.,
emph{Theory and Applications of Fractional Differential Equations},
Elsevier B. V., Amsterdam, 2006.
Kumar, A., Chauhan, H.V., Ravichandran, C., Nisar, K.S., Baleanu, D.,
emph{Existence of solutions of non-autonomous fractional differential equations with
integral impulse condition},
Adv. Differential Equations, (2020), 2020:434.
Kumar, A., Pandey, D.N.,
emph{Existence of mild solution of Atangana-Baleanu fractional differential equations
with non-instantaneous impulses and with non-local conditions},
Chaos Solitons Fractals, textbf{132}(2020), 109551.
Liu, K., Wang, J., O'Regan, D., Fev{c}kan, M.,
emph{A new class of $(omega, c)$-periodic non-instantaneous impulsive differential equations},
Mediterr. J. Math., (2020), textbf{17}:155.
Luo, D., Luo, Z.,
emph{Existence of solutions for fractional differential inclusions with initial value
condition and non-instantaneous impulses},
Filomat, textbf{33}(17)2019), 5499-5510.
Myshkis, A.D., Samoilenko, A.M.,
emph{Systems with impulsive at fixed moments of time},
Mat. Sb., textbf{74}(1967), 202-208.
Ngo, V.H., O'Regan, D.,
emph{A remark on $psi$-Hilfer fractional differential equations with non-instantaneous impulses},
Math. Methods Appl. Sci., (2020), 1-15.
Podlubny, I.,
emph{Fractional Differential Equations},
Academic Press, San Diego, 1999.
Samko, S., Kilbas, A., Marichev, O.,
emph{Fractional Integrals and Derivatives},
Gordon and Breach Science Publishers, Longhorne, PA, 1993.
Srivastava, H.M., Saad, K.M.,
emph{Some new models of the time-fractional gas dynamics equation},
Adv. Math. Models Appl., {bf 3}(1)(2018), 5-17.
Zada, A., Ali, N., Riaz, U.,
emph{Ulam's stability of multi-point implicit boundary value problems with non-instantaneous impulses},
Boll. Unione Mat. Ital., textbf{13}(2020), 305-328.
Zhao, Y., Luo, C., Chen, H.,
emph{Existence results for non-instantaneous impulsive nonlinear fractional differential
equation via variational methods},
Bull. Malays. Math. Sci. Soc., textbf{43}(2020), 2151-2169.
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