Analysis of RLC multi-term fractional boundary value problems

[1] M. Al-Refai, Basic results on nonlinear eigenvalue problems of fractional order, Electron. J. Differ. Equ. 2012 (2012), 1-12. Search in Google Scholar

[2] M. Al-Refai, K. Pal, A maximum principle for a fractional boundary value problem with convection term and applications, Math. Model. Anal. 24 (2018), 62-71. Search in Google Scholar

[3] O. Brandibur, E. Kaslik, Stability properties of multi-term fractional-differential equations, Fractal Fract. 7 (2023), 117. Search in Google Scholar

[4] P. Eloe, J. Neugebauer, Green’s functions for a fractional boundary value problem with three terms, Foundations 2 (2022), 885-897. Search in Google Scholar

[5] J. L. Gracia, E. O’Riordan, M. Stynes, Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann-Liouville-Caputo fractional derivative, BIT Numer. Math. 60 (2020), 411-439. Search in Google Scholar

[6] J. L. Gracia, M. Stynes, Formal consistency versus actual convergence rates of difference schemes for fractional-derivative boundary value problems, Fract. Calc. Appl. Anal. 18 (2015), 419-436. Search in Google Scholar

[7] J. L. Gracia, M. Stynes, A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative, J. Comput. Appl. Math. 381 (2021), 113020. Search in Google Scholar

[8] J. L. Gracia, M. Stynes, A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution, Comput. Appl. Math. 43 (2024), 199. Search in Google Scholar

[9] J. Graef, L. Kong, Q. Kong, M. Wang, Positive solutions of nonlocal fractional boundary value problems, Discrete Contin. Dyn. Syst. 2013 (2013), 282-290. Search in Google Scholar

[10] J. Graef, L. Kong, Q. Kong, M. Wang., On a fractional boundary value problem with a perturbation term, J. Appl. Anal. Comput. 7 (2017), 57-66. Search in Google Scholar

[11] A. Guezane-Lakoud, S. Bensebaa, Solvability of a fractional boundary value problem with fractional derivative condition, Arab. J. Math. 3 (2014), 39-48. Search in Google Scholar

[12] A. Guezane-Lakoud, R. Khaldi, D. F. M. Torres, On a fractional oscillator equation with natural boundary conditions, Prog. Fract. Differ. Appl. 3 (2017), 1-7. Search in Google Scholar

[13] B. Ibrahim, Q.-X. Dong, Z. Fan, Existence for boundary value problems of two-term Caputo fractional differential equations, J. Nonlinear Sci. Appl. 10 (2017), 511-520. Search in Google Scholar

[14] L. Jia, H. Chen, V. Ervin, Existence and regularity of solutions to 1-D fractional order diffusion equations, preprint, arXiv: 1808.10555. Search in Google Scholar

[15] R. Khaldi, A. Guezane-Lakoud, Upper and lower solutions method for higher order boundary value problems, Prog. Fract. Differ. Appl. 3 (2017), 53-57. Search in Google Scholar

[16] R. Khaldi, A. Guezane-Lakoud, On generalized nonlinear Euler-Bernoulli beam type equations, Acta Univ. Sapientiae, Math. 10 (2018), 90-100. Search in Google Scholar

[17] A. Kilbas, H. Srivastava, J.Trujillo, Theory and applications of fractional differential equations, Elsevier Amsterdam, 2006. Search in Google Scholar

[18] X. Meng, M. Stynes, The Green’s function and a maximum principle for a Caputo two-point boundary value problem with a convection term, J. Math. Anal. Appl. 461 (2018), 198-218. Search in Google Scholar

[19] J. Rong, C. Bai, Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions, Adv. Difference Equ. 2015 (2015), 82. Search in Google Scholar

[20] B. Sambandham, A. Vatsala, Basic results for sequential Caputo fractional differential equations, Mathematics 3 (2015), 76-91. Search in Google Scholar

[21] S. Samko, A. Kilbas, O. Marichev, Fractional integrals and derivatives, Taylor & Francis, 1993. Search in Google Scholar

[22] A. Souahi, A. Guezane-Lakoud, A. Hitta, Positive solutions for higher-order nonlinear fractional differential equations, Vietnam J. Math. 45 (2017), 441-450. Search in Google Scholar

[23] S. Stanek, Periodic problem for two-term fractional differential equations, Fract. Calc. Appl. Anal. 20 (2017), 662-678. Search in Google Scholar

[24] M. Stynes, J. L. Gracia, A finite difference method for a two-point boundary value problem with a Caputo fractional derivative, IMA J. Numer. Anal. 35 (2015), 698-721. Search in Google Scholar

[25] A. Vatsala, G. Pageni, V. Vijesh, Analysis of sequential Caputo fractional differential equations versus non-sequential Caputo fractional differential equations with applications, Foundations 2 (2022), 1129-1142. Search in Google Scholar

[26] O. K. Wanassi, F. Toumi, Existence results for perturbed boundary value problem with fractional order, Ric. Mat. 73 (2024), 1367-1383. Search in Google Scholar

[27] H. Wang, D. Yang, Wellposedness of Neumann boundary-value problems of space-fractional differential equations, Fract. Calc. Appl. Anal. 20 (2017), 1356-1381. Search in Google Scholar

[28] Y. Wei, Z. Bai, Solvability of some fractional boundary value problems with a convection term, Discrete Dyn. Nat. Soc. 2019 (2019), 1230502. Search in Google Scholar

[29] C. Xie, S. Fang, Finite difference scheme for timespace fractional diffusion equation with fractional boundary conditions, Math. Methods Appl. Sci. 43 (2020), 3473-3487. Search in Google Scholar