On conformable fractional differential equations with nonlocal-impulsive conditions
DOI:
https://doi.org/10.5269/bspm.76296Resumen
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.
Referencias
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[2] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279(2015), 57-66.
[3] 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.
[4] M. Bouaouid, K. Hilal, S. Melliani, Nonlocal telegraph equation in frame of the conformable time-fractional derivative, Advances in Mathematical Physics 2019(2019).
[5] M. Bouaouid, M. Atraoui, K. Hilal and S. Melliani, Fractional differential equations with nonlocal-delay condition, J. Adv. Math. Stud 11(2018), 214-225.
[6] M. Bouaouid, K. Hilal, S. Melliani, Sequential evolution conformable differential equations of second order with nonlocal condition, Advances in Difference Equations (2019), 2019:21.
[7] 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.
[8] 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.
[9] K. Deng, Exponetial decay of solutions of semilinear parabolic equations with nonlocal initial conditions, Journal of Mathematical Analysis and Applications 179(1993), 630-637.
[10] W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10(1997), 89-94.
[11] A. Zavalishchin, Impulse dynamic systems and applications to mathematical economics, Dynam. Systems Appl. 3(1994), 443-449.
[12] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
[13] G.M. Mophou, Existence and uniqueness of integral solutions to impulsive fractional differential equations, Nonlinear Analysis 72(2010), 1604-1615.
[14] 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.
[15] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel Journal of Mathematics, 59(1987), 327-352.
[16] H. Kellerman and M. Hieber, Integrated semigroups, Journal of Functional Analysis 84(1989), 160-180.
[17] H.R. Thieme, "Integrated semigroups" and integrated solutions to abstract Cauchy problems, Journal of mathematical analysis and applications 152(1990), 416-447.
[18] 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.
[19] A. Pazy, Semigropus of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
[2] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279(2015), 57-66.
[3] 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.
[4] M. Bouaouid, K. Hilal, S. Melliani, Nonlocal telegraph equation in frame of the conformable time-fractional derivative, Advances in Mathematical Physics 2019(2019).
[5] M. Bouaouid, M. Atraoui, K. Hilal and S. Melliani, Fractional differential equations with nonlocal-delay condition, J. Adv. Math. Stud 11(2018), 214-225.
[6] M. Bouaouid, K. Hilal, S. Melliani, Sequential evolution conformable differential equations of second order with nonlocal condition, Advances in Difference Equations (2019), 2019:21.
[7] 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.
[8] 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.
[9] K. Deng, Exponetial decay of solutions of semilinear parabolic equations with nonlocal initial conditions, Journal of Mathematical Analysis and Applications 179(1993), 630-637.
[10] W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10(1997), 89-94.
[11] A. Zavalishchin, Impulse dynamic systems and applications to mathematical economics, Dynam. Systems Appl. 3(1994), 443-449.
[12] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
[13] G.M. Mophou, Existence and uniqueness of integral solutions to impulsive fractional differential equations, Nonlinear Analysis 72(2010), 1604-1615.
[14] 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.
[15] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel Journal of Mathematics, 59(1987), 327-352.
[16] H. Kellerman and M. Hieber, Integrated semigroups, Journal of Functional Analysis 84(1989), 160-180.
[17] H.R. Thieme, "Integrated semigroups" and integrated solutions to abstract Cauchy problems, Journal of mathematical analysis and applications 152(1990), 416-447.
[18] 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.
[19] A. Pazy, Semigropus of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
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Publicado
2025-09-22
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Research Articles
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Cómo citar
Malouh, M. ., Bouaouid, M., & Elomari, M. . (2025). On conformable fractional differential equations with nonlocal-impulsive conditions. Boletim Da Sociedade Paranaense De Matemática, 43, 1-13. https://doi.org/10.5269/bspm.76296
