پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 717 |
| تعداد مقالات | 10,307 |
| تعداد مشاهده مقاله | 72,269,776 |
| تعداد دریافت فایل اصل مقاله | 63,999,666 |
Solutions of fractional functional integrodifferential equations via Petryshyn’s fixed point theorem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 9، دوره 16، شماره 6، شهریور 2025، صفحه 93-105 اصل مقاله (416.47 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33112.4930 | ||
| نویسندگان | ||
| Mohamed Metwali1؛ Manochehr Kazemi* 2؛ Alireza Yaghoobnia3 | ||
| 1Department of Mathematics, Faculty of Science, Damanhour University, Egypt | ||
| 2Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran | ||
| 3Department of mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran | ||
| تاریخ دریافت: 09 بهمن 1402، تاریخ بازنگری: 15 فروردین 1403، تاریخ پذیرش: 19 فروردین 1403 | ||
| چکیده | ||
| This article provides the presence of solutions to a fractional functional integro-differential equation via measures of non-compactness. We present and prove a novel theorem that guarantees the existence of solutions, employing Petryshyn's fixed point theorem in the space of continuous functions. These findings build upon previous studies by establishing the existence of results under less stringent conditions. Furthermore, we provide illustrative examples of such equations to showcase the efficacy of the obtained results. | ||
| کلیدواژهها | ||
| Measures of non-compactness؛ Fractional functional integro-differential equation؛ Fixed point theorem؛ Existence of solutions | ||
| مراجع | ||
|
[1] R.P. Agarwal, Y. Zhou, and Y. He, Existence of fractional neutral functional differential equations, Comput. Math. Appl. 59 (2010), no. 3, 1095–1100. [2] A. Aghajani, Y. Jalilian, and J.J. Trujillo, On the existence of solutions of fractional integro-differential equations, Fract. Cal. Appl. Anal. 15 (2012), no. 1, 44–69. [3] B. Ahmad, S.K. Ntouyas, R.P. Agarwal, and A. Alsaedi, Existence results for sequential fractional integro-differential equations with nonlocal multi-point and strip conditions, Boundary Value Prob. 2016 (2016), no. 1, 1–16. [4] A. Anguraj, P. Karthikeyan, and J.J. Trujillo, Existence of solutions to fractional mixed integrodifferential equations with nonlocal initial condition, Adv. Differ. Equ. 2011 (2011), 1–12. [5] R. Azimi, M. Mohagheghy Nezhad, and S. Foadian, Shifted Legendre Tau method for solving the fractional stochastic integro-differential equations, Glob. Anal. Discrete Math. 6 (2021), no. 2, 221–241. [6] M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), no. 2, 1340–1350. [7] P. Borisut, P. Kumam, I. Ahmed, and K. Sitthithakerngkiet, Stationarity–conservation laws for fractional differential equations with variable coefficients, J. Phys. A: Math. Gen. 35 (2002), no. 31, 6675. [8] S. Dadsetadi, K. Nouri, and L. Torkzadeh, Solvability of some nonlinear integro-differential equations of fractional order via measure of non-compactness, Pure Appl. Math. 27 (2020), no. 1, 13–24. [9] A. Deep and M. Kazemi, Solvability for 2D non-linear fractional integral equations by Petryshyns fixed point theorem, J. Comput. Appl. Math. 444 (2024), 115797. [10] A. Deep, Deepmala, and J. Rezaei Roshan, Solvability for generalized nonlinear functional integral equations in Banach spaces with applications, J. Integral Equ. Appl. 33 (2021), no. 1, 19–30. [11] A. Deep, D. Saini, H. Kumar Singh, and U Cakan, Solvability for fractional integral equations via Petryshyns fixed-point theorem, J. Integral Equ. Appl. 35 (2023), no. 3, 277–289. [12] L.S. Goldenshtejn and A.S. Markus, On the measure of non-compactness of bounded sets and of linear operators, Studies in Algebra and Math. Anal. (Russian), Izdat. “Karta Moldovenjaske”, Kishinev, 1965, pp. 45–54. [13] J. Henderson and R. Luca, Existence of nonnegative solutions for a fractional integro-differential equation, Results Math. 72 (2017), no. 1, 747–763. [14] R.W. Ibrahim, Existence of iterative Cauchy fractional differential equation, J. Math. 2012 (2012). [15] K. Karthikeyan and J.J. Trujillo, Existence and uniqueness results for fractional integro-differential equations with boundary value conditions, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4037–4043. [16] M. Kazemi and R. Ezzati, Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness, Appl. Math. Comput. 275 (2016), 165–171. [17] M. Kazemi, H. Chaudhary, and A. Deep, Existence and approximate solutions for Hadamard fractional integral equations in a Banach space, J. Integral Equ. Appl. 35 (2023), no. 1, 27–40. [18] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006. [19] K. Kuratowski, K. Sur les espaces completes, Fund. Math. 15 (1934), 301–335. [20] A. Lachouri, A. Ardjouni, and A. Djoudi, Existence results for integral boundary value problems of fractional differential equations with two nonlinear terms in Banach spaces, Bull. Int. Math. Virtual Inst. 11 (2021), no. 1, 159–168. [21] A.B. Malinowska, M.R.S. Ammi, and D.F.M. Torres, Composition functionals in fractional calculus of variations, arXiv preprint arXiv:1009.2671, 2010. [22] M.M.A. Metwali and S.A.M. Alsallami, Discontinuous solutions of delay fractional integral equation via measures of noncompactness, AIMS Math. 8 (2023), no. 9, 21055–21068. [23] M.M.A. Metwali, On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order, J. Math. Appl. 40 (2017), 121–134. [24] M.M.A. Metwali, Solvability in weighted L1-spaces for the m-product of integral equations and model of the dynamics of the capillary rise, J. Math. Anal. Appl. 515 (2022), no. 2, 126461. [25] K. Nouri, M. Nazari, and B. Keramati, Existence results for a coupled system of fractional integro-differential equations with time-dependent delay, J. Fixed Point Theory Appl. 19 (2017), no. 4, 2927–2943. [26] K. Nouri, D. Baleanu, and L. Torkzadeh, Study on application of hybrid functions to fractional differential equations, Iran. J. Sci. Technol. Trans. A: Sci. 42 (2018), no. 3, 1343–1350. [27] R.D. Nussbaum, The fixed-point index and fixed point theorem for k-set contractions, PhD Thesis, The University of Chicago, ProQuest LLC, Ann Arbor, MI, 1969. [28] W.V. Petryshyn, Structure of the fixed points sets of k-set-contractions, Arch. Ration. Mech. Anal. 40 (1970/1971), 312–328. [29] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, USA, 1999. [30] C. Ravichandran and D. Baleanu, Existence results for fractional neutral functional integro-differential evolution equations with infinite delay in Banach spaces, Adv. Differ. Equ. 2013 (2013), no. 1, 1–12. [31] P. Saini, U. Cakan, and A. Deep, Existence of solutions for 2D nonlinear fractional Volterra integral equations in Banach Space, Rocky Mount. J. Math. 53 (2023), no. 6, 1965–1981. [32] S.P. Singh, B. Watson, and P. Srivastava, Fixed Point Theory and Best Approximation: The KKM-Map Principle, Springer Science & Business Media, 2013. [33] D.N. Susahab, S. Shahmorad, and M. Jahanshahi, Efficient quadrature rules for solving nonlinear fractional integro-differential equations of the Hammerstein type, Appl. Math. Modell. 39 (2015), no. 18, 5452–5458. [34] S. Unhaley and S. Kendre, On existence and uniqueness results for iterative fractional integro-differential equation with deviating arguments, Appl. Math. E-Notes 19 (2019), 116–127. [35] D. Yang and W. Zhang, Solutions of equivariance for iterative differential equations, Appl. Math. Lett. 17 (2004), no. 7, 759–765. [36] L. Zhang, B. Ahmad, G.Wang, and R.P. Agarwal, Nonlinear fractional integro-differential equations on unbounded domains in a Banach space, J. Comput. Appl. Math. 249 (2013), 51–56. | ||
|
آمار تعداد مشاهده مقاله: 1,649 تعداد دریافت فایل اصل مقاله: 744 |
||