پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 677 |
| تعداد مقالات | 9,871 |
| تعداد مشاهده مقاله | 69,991,647 |
| تعداد دریافت فایل اصل مقاله | 49,279,521 |
A certain coupled system of $q$-FDEs on two consecutive intervals under Dirichlet conditions via Krasnoselskii's theorem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 05 مهر 1404 اصل مقاله (534.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.34514.5154 | ||
| نویسندگان | ||
| Mohammad Esmael Samei* 1؛ Mohammad Izadi2؛ Mohammed K. A. Kaabar3 | ||
| 1Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran | ||
| 3Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia | ||
| تاریخ دریافت: 01 تیر 1403، تاریخ پذیرش: 24 بهمن 1403 | ||
| چکیده | ||
| In this study, we use certain mathematical tools to analyze the solutions of a system of fractional $q$-differential equation ${}^C\mathbb{D}_{q}^{\sigma_i} [\wp](\mathfrak{t}) = \mathfrak{w}_i( \mathfrak{t}, \wp(\mathfrak{t}), {}^C\mathbb{D}_{q}^{{}_i\nu_{j}} [\wp](\mathfrak{t}), \mathbb{I}_{q}^{{}_{i}\nu_j} [\wp] (\mathfrak{t}) )$, $i=~1$ whenever $\mathfrak{t} \in [0, \mathfrak{t}_0]$, and $i=2$ whenever $\mathfrak{t} \in [\mathfrak{t}_0, 1]$, for $j=1,2$, such as fixed point theorem of Krasnoselskii and Banach contraction principle, under simultaneous Dirichlet boundary conditions. Here, we use standard definitions of the Liouville-Caputo fractional type $q-$derivative and Riemann-Liouville $q-$integral. Some illustrative examples with numerical results are discussed, too. | ||
| کلیدواژهها | ||
| nonlinear fractional equation؛ fractional $q-$differential equation؛ Dirichlet boundary conditions؛ Riemann--Liouville $q-$integral | ||
| مراجع | ||
|
[1] T. Abdeljawad, J. Alzabut, and D. Baleanu, A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems, J. Inequal. Appl. 216 (2016), 240. [2] C.R. Adams, The general theory of a class of linear partial q-difference equations, Trans. Amer. Math. Soc. 26 (1924), 283–312. [3] R.P. Agarwal, D. Baleanu, V. Hedayati, and S. Rezapour, Two fractional derivative inclusion problems via integral boundary condition, Appl. Math. Comput. 257 (2015), 205–212. [4] B. Ahmad, M. Alghanmi, A. Alsaedi, H.M. Srivastava, and S.K. Ntouyas, The Langevin equation in terms of generalized Liouville-Caputo derivatives with nonlocal boundary conditions involving a generalized fractional integral, Mathematics 7 (2019), no. 6, 533. [5] B. Ahmad, J.J. Nieto, A. Alsaedi, and H. Al-Hutami, Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions, J. Franklin Inst. 351 (2014), 2890–2909. [6] M.H. Annaby and Z.S. Mansour, q-Fractional Calculus and Equations, Springer Heidelberg, Cambridge, 2012. [7] Z. Baitiche, C. Derbazi, J. Alzabut, M.E. Samei, M.K.A. Kaabar, and Z. Siri, Monotone iterative method for Langevin equation in terms of ψ-Caputo fractional derivative and nonlinear boundary conditions, Fractal Fractional 5 (2021), no. 2, 81. [8] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhäuser, Boston, 2001. [9] A. Bonfanti, J.L. Kaplan, G. Charras, and A. Kabla, Fractional viscoelastic models for power-law materials, Soft Matter. 16 (2020), 6002–6020. [10] J. Danane, K. Allali, and Z. Hammouch, Mathematical analysis of a fractional differential model of HBV infection with antibody immune response, Chaos Solit. Fract. 136 (2020), 109787. [11] S. Djilali, B. Ghanbari, and W. Adel, The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative, Adv. Differ. Equ. 2021 (2021), 20. [12] R.A.C. Ferreira, Nontrivials solutions for fractional q-difference boundary value problems, Electronic J. Qualit. Theory Differ. Equ. 70 (2010), 1–101. [13] M. Izadi, N. Sene, W. Adel, and A. El-Mesady, The Layla and Majnun mathematical model of fractional order: Stability analysis and numerical study, Results Phys. 51 (2023), 106650. [14] M. Izadi, S. Yuzbasi, and W. Adel, Accurate and efficient matrix techniques for solving the fractional Lotka-Volterra population model, Phys. A 600 (2022), 127558. [15] F.H. Jackson, q-difference equations, Amer. J. Math. 32 (1910), 305–314. [16] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2004. [17] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [18] S. Qureshi, A. Yusuf, A.A. Shaikh, M. Inc, and D. Baleanu, Fractional modeling of blood ethanol concentration system with real data application, Chaos 29 (2019), 013143. [19] P.M. Rajkovic, S.D. Marinkovic, and M.S. Stankovic, Fractional integrals and derivatives in q-calculus, Appl. Anal. Discrete Math. 1 (2007), 311–323. [20] S. Rezapour and H. Mohammadi, SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order, Adv. Differ. Equ. 2020 (2022), 490. [21] S. Rezapour and M.E. Samei, On the existence of solutions for a multi-singular pointwise defined fractional q-integro-differential equation, Boundary Value Problems 2020 (2020), 38. [22] M.E. Samei, R. Ghaffari, S.W. Yao, M.K.A. Kaabar, F. Martınez, and M. Inc, Existence of solutions for a singular fractional q-differential equations under Riemann-Liouville integral boundary condition, Symmetry 13 (2021), 135. [23] M.E. Samei and S. Rezapour, On a system of fractional q-differential inclusions via sum of two multi-term functions on a time scale, Boundary Value Problems 2020 (2020), 135. [24] M.E. Samei and W. Yang, Existence of solutions for k-dimensional system of multi-term fractional q-integro-differential equations under anti-periodic boundary conditions via quantum calculus, Math. Modell. Appl. Sci. 43 (2020), no. 7, 4360–4382. [25] M. Shabibi, Z. Zeinalabedini Charandabi, H. Mohammadi, and S. Rezapour, Investigation of mathematical model of human liver by Caputo fractional derivative approach, J. Adv. Math. Model. 11 (2021), 750–760. [26] D.R. Smart, Fixed Point Theorems, Cambridge University Press, New York, 1980. [27] H.M. Srivastava, An introductory overview of fractional-calculus operators based upon the Fox-Wright and related higher transcendental functions, J. Adv. Engrg. Comput. 5 (2021), 135–166. [28] H.M. Srivastava, Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformations, J. Nonlinear Convex Anal. 22 (2021), 1501–1520. [29] S. Yuzbasi and M. Izadi, Bessel-quasilinearization technique to solve the fractional-order HIV-1 infection of CD4+T-cells considering the impact of antiviral drug treatment, Appl. Math. Comput. 431 (2022), 127319. [30] Y. Zhao, H. Chen, and Q. Zhang, Existence results for fractional q-difference equations with nonlocal q–integral boundary conditions, Adv. Differ. Equ. 2013 (2013), 48. [31] H. Zhou, J. Alzabut, and L. Yang, On fractional Langevin differential equations with anti-periodic boundary conditions, Eur. Phys. J. Spec. Topics 226 (2017), 3577–3590. | ||
|
آمار تعداد مشاهده مقاله: 597 تعداد دریافت فایل اصل مقاله: 163 |
||