Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators
-
Jaouad El Matloub
and
Khalil Ezzinbi
Abstract
In this work, we mainly focus on the local existence and regularity of integral solutions for a class of nondensely defined partial neutral functional integrodifferential equations with unbounded delay. We use the theory of integrated resolvent operators introduced by Oka [H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 1995, 2, 193–232]. Finally, we provide an example to demonstrate the basic findings of our work.
Acknowledgements
The authors would like to express their deep gratitude for the anonymous reviewers for their efforts in improving the manuscript.
References
[1] M. Adimy, H. Bouzahir and K. Ezzinbi, Local existence for a class of partial neutral functional differential equations with infinite delay, Differ. Equ. Dyn. Syst. 12 (2004), no. 3–4, 353–370. 10.32917/hmj/1150998507Search in Google Scholar
[2] M. Adimy and K. Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain, J. Differential Equations 147 (1998), no. 2, 285–332. 10.1006/jdeq.1998.3446Search in Google Scholar
[3] M. Adimy and K. Ezzinbi, Strict solutions of nonlinear hyperbolic neutral differential equations, Appl. Math. Lett. 12 (1999), no. 1, 107–112. 10.1016/S0893-9659(98)00134-7Search in Google Scholar
[4] K. Balachandran and R. Sakthivel, Existence of solutions of neutral functional integrodifferential equation in Banach spaces, Proc. Indian Acad. Sci. Math. Sci. 109 (1999), no. 3, 325–332. 10.1007/BF02843536Search in Google Scholar
[5] W. Desch, R. Grimmer and W. Schappacher, Well-posedness and wave propagation for a class of integrodifferential equations in Banach space, J. Differential Equations 74 (1988), no. 2, 391–411. 10.1016/0022-0396(88)90011-3Search in Google Scholar
[6] M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Ration. Mech. Anal. 31 (1968), no. 2, 113–126. 10.1007/BF00281373Search in Google Scholar
[7] J. K. Hale, Functional differential equations with infinite delays, J. Math. Anal. Appl. 48 (1974), 276–283. 10.1016/0022-247X(74)90233-9Search in Google Scholar
[8] E. Hernández, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), no. 1, 194–210. 10.1016/j.jmaa.2003.11.052Search in Google Scholar
[9] Y. Hino, S. Murakami and T. Naito, Functional-Differential Equations with Infinite Delay, Lecture Notes in Math. 1473, Springer, Berlin, 2006. Search in Google Scholar
[10] T. Naito, On autonomous linear functional differential equations with infinite retardations, J. Differential Equations 21 (1976), no. 2, 297–315. 10.1016/0022-0396(76)90124-8Search in Google Scholar
[11] T. Naito, On linear autonomous retarded equations with an abstract phase space for infinite delay, J. Differential Equations 33 (1979), no. 1, 74–91. 10.1016/0022-0396(79)90081-0Search in Google Scholar
[12] H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 (1995), no. 2, 193–232. 10.1216/jiea/1181075869Search in Google Scholar
[13] K. Schumacher, Existence and continuous dependence for functional-differential equations with unbounded delay, Arch. Ration. Mech. Anal. 67 (1978), no. 4, 315–335. 10.1007/BF00247662Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- New analytical technique to solve fractional-order Sharma–Tasso–Olver differential equation using Caputo and Atangana–Baleanu derivative operators
- Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators
- On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations
- On ℐ2(𝒮θ p,r )-summability of double sequences in neutrosophic normed spaces
- Earthquake convexity and some new related inequalities
- On λ-statistically φ-convergence
- Multivalued relation-theoretic weak contractions and applications
- Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup
- Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations
- Existence and linear independence theorem for linear fractional differential equations with constant coefficients
- A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space
- Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion
- On statistical convergence of order α of sequences in gradual normed linear spaces
- Uniqueness of meromorphic functions and their powers in set sharing
- Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results
- Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions
- Multiple solitons, periodic solutions and other exact solutions of a generalized extended (2 + 1)-dimensional Kadomstev--Petviashvili equation
Articles in the same Issue
- Frontmatter
- New analytical technique to solve fractional-order Sharma–Tasso–Olver differential equation using Caputo and Atangana–Baleanu derivative operators
- Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators
- On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations
- On ℐ2(𝒮θ p,r )-summability of double sequences in neutrosophic normed spaces
- Earthquake convexity and some new related inequalities
- On λ-statistically φ-convergence
- Multivalued relation-theoretic weak contractions and applications
- Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup
- Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations
- Existence and linear independence theorem for linear fractional differential equations with constant coefficients
- A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space
- Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion
- On statistical convergence of order α of sequences in gradual normed linear spaces
- Uniqueness of meromorphic functions and their powers in set sharing
- Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results
- Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions
- Multiple solitons, periodic solutions and other exact solutions of a generalized extended (2 + 1)-dimensional Kadomstev--Petviashvili equation
