DOI: 10.12732/ijam.v37i2.7
NON-INSTANTANEOUS PERIODIC
BVP OF FRACTIONAL
VOLTERRA-FREDHOLM MODELS
Saif Aldeen M. Jameel 1,§ , Esraa A. Hussein 2
1,2 Department of Statistics Techniques
Middle Technical University
Institute of Administration Rusafa
Baghdad-10045,
IRAQ
Abstract. In this manuscript, we study the sufficient conditions for existence results of PC-mild solutions of non-instantaneous impulses Caputo fractional Volterra-Fredholm integro-differential equations with periodic boundary conditions. Fractional calculus, semigroup theory, Krasnoselskii and Sadovskii fixed point theorems are used to prove the existence results. Moreover, an example is finally presented.
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DOI: 10.12732/ijam.v37i2.7
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 2
References
[1] M. Alesemi, N. Iqbal and A. A. Hamoud, The analysis of fractional order proportional delay physical models via a novel transform, Complexity, 2022 (2022), 1-13.
[2] S. Abbas, M. Benchohra, Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses, Appl. Math. Comput., 257 (2015), 190-198.
[3] P. Chen, X. Zhang, Y. Li, Non-autonomous parabolic evolution equations with noninstantaneous impulses governed by noncompact evolution families, J. Fixed Point Theory Appl., 21, No 3 (2019), 84-101.
[4] A. Debbouche, D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl., 62 (2011), 1442-1450.
[5] F. Ge, H. Zhou, C. Kou, Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique, Appl. Math. Comput., 275 (2016), 107-120.
[6] H. Gou, B. Li, Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 204-214.
[7] A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra-Fredholm integro differential equations, Adv. Theory Nonlinear Anal. Appl., 4, No 4 (2020), 321-331.
[8] A. Hamoud, S. A. M. Jameel, N. M. Mohammed, H. Emadifar, F. Parvaneh, and M. Khademi,
On controllability for fractional Volterra-Fredholm system, Nonlinear Functional Analysis and Applications (2023), 407-420.
[9] A. Hamoud, K. Ghadle, Giniswamy, and M. Sh. B. Issa, Existence and uniqueness theorems for fractional Volterra-Fredholm integro-differential equations, International Journal of Applied Mathematics, 31, No 3 (2018), 333-348; DOI: 10.12732/ijam.v31i3.3.
[10] A. Hamoud, and K. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations, J. Appl. Comput. Mech., 5, No 1 (2019), 58-69.
[11] A.A. Hamoud, N.M. Mohammed, R. Shah, Theoretical analysis for a system of nonlinear
R-Hilfer fractional Volterra-Fredholm integro-differential equations, J. Sib. Fed. Univ. Math. Phys., 16, No 2 (2023), 216-229.
[12] E. Hernandez, D. O’Regan, On a new class of abstract impulsive differential equations, Proc. Am. Math. Soc., 141 (2013), 1641-1649.
[13] S. A. M. Jameel, S. Abdul Rahmn, and A. A. Hamoud, Analysis of Hilfer fractional Volterra-Fredholm system, Nonlinear Functional Analysis and Applications (2024), 259-273.
[14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).
[15] H. Li, Y. Kao, Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses, Appl. Math. Comput., 361 (2019), 22-31.
[16] L. Liu, F. Guo, Y. Wu, Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces, J. Math. Anal. Appl., 309 (2005), 638-649.
[17] L. Liu, Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces, Nonlinear Anal., 42 (2000), 583-598.
[18] Y. Liu, Piecewise continuous solutions of initial value problems of singular fractional differential equations with impulse effects, Acta Math. Sci., 36B (2016), 1492-1508.
[19] M. Malik, V. Kumar, Existence, uniqueness and UHR stability of solutions to nonlinear ordinary differential equations with noninstantaneous impulses, IMA J. Math. Control Inf., 37, No 1 (2020), 276-299.
[20] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press, New York/London/Toronto (1999).
[21] M. Pierri, D. O’Regan, V. Rolnik, Existence of solutions for semilinear abstract differential equations with not instantaneous impulses, Appl. Math. Comput., 219 (2013), 6743-6749.
[22] Y. Tian, J. Wang, Y. Zhou, Almost periodic solutions for a class of noninstantaneous
impulsive differential equations, Quaest. Math., 42, No 7 (2019), 885-905.
[23] J. Wang, X. Li, Periodic BVP for integer/fractional order nonlinear differential equations with noninstantaneous impulses, Appl. Math. Comput., 46 (2014), 321-334.
[24] Z. Yan, F. Lu, Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay, Appl. Math. Comput., 292 (2017), 425-447.
[25] X. Yang, C. Li, T. Huang, Q. Song, Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses, Appl. Math. Comput., 293 (2017), 416-422.
[26] X. Yu, J. Wang, Periodic boundary value problems for nonlinear impulsive evolution equations on Banach spaces, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 980-989.
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