On conformable fractional differential equations with nonlocal-impulsive conditions

Mahacine  Malouh; Mohamed Bouaouid; M’hamed  Elomari

doi:10.5269/bspm.76296

Mahacine Malouh
Mohamed Bouaouid Sultan Moulay Slimane University, Beni Mellal, Morocco.
M’hamed Elomari

Abstract

This paper addresses the existence and controllability of the integral solution to a nondense conformable fractional differential equation with a nonlocal-impulsive condition. The main findings are derived using fixed-point theorems in conjunction with the theory of integrated semigroups.

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References

R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264(2014), 65-70.

T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279(2015), 57-66.

M. Bouaouid, K. Hilal and S. Melliani, Existence of integral solutions for conformable fractional differential equations with nonlocal conditions, Rocky Mountain Journal of Mathematics, 50(2020), 871âC“879.

M. Bouaouid, K. Hilal, S. Melliani, Nonlocal telegraph equation in frame of the conformable time-fractional derivative, Advances in Mathematical Physics 2019(2019).

M. Bouaouid, M. Atraoui, K. Hilal and S. Melliani, Fractional differential equations with nonlocal-delay condition, J. Adv. Math. Stud 11(2018), 214-225.

M. Bouaouid, K. Hilal, S. Melliani, Sequential evolution conformable differential equations of second order with nonlocal condition, Advances in Difference Equations (2019), 2019:21.

H. Eltayeb, I. Bachar and M. Gad-Allah, Solution of singular one-dimensional Boussinesq equation by using double conformable Laplace decomposition method, Advances in Difference Equations (2019), 2019:293.

L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications 162(1991), 494-505.

K. Deng, Exponetial decay of solutions of semilinear parabolic equations with nonlocal initial conditions, Journal of Mathematical Analysis and Applications 179(1993), 630-637.

W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10(1997), 89-94.

A. Zavalishchin, Impulse dynamic systems and applications to mathematical economics, Dynam. Systems Appl. 3(1994), 443-449.

V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.

G.M. Mophou, Existence and uniqueness of integral solutions to impulsive fractional differential equations, Nonlinear Analysis 72(2010), 1604-1615.

J. Liang, J.H. Liu and T-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Mathematical and Computer Modelling 49(2009), 798-804.

W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel Journal of Mathematics, 59(1987), 327-352.

H. Kellerman and M. Hieber, Integrated semigroups, Journal of Functional Analysis 84(1989), 160-180.

H.R. Thieme, "Integrated semigroups" and integrated solutions to abstract Cauchy problems, Journal of mathematical analysis and applications 152(1990), 416-447.

M. Adimy, M. Alia and K. Ezzinbi: Functional differential equations with unbounded delay in extrapo-lation spaces, Electron. J. Dier. Equ. Conf. 2014(2014), 1-16.

A. Pazy, Semigropus of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.