References
- P. Agarwal, E. Karimov, M. Mamchuev and M. Ruzhansky. On boundary-value problems for a partial differential equation with Caputo and Bessel operators, 2016.
- R.P. Agarwal, D. Baleanu, V. Hedayati and Sh. Rezapour. Two fractional derivative inclusion problems via integralboundary condition. Appl. Math. Comput., 257:205–212, 2015. https://doi.org/10.1016/j.amc.2014.10.082.
- B. Ahmad and J.J. Nieto. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Boundary Value Problems, 2009. https://doi.org/10.1155/2009/708576.
- B. Ahmad, J.J. Nieto and J. Pimentel. Some boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl., 62(3):1238–1250, 2011. https://doi.org/10.1016/j.camwa.2011.02.035. doi: 10.1016/j.camwa.2011.02.035
- A. Alsaedi, S.K. Ntouyas, R.P. Agarwal and B. Ahmad. On Caputo type sequential fractional differential equations with nonlocal integral boundary conditions. Adv. Differ. Equ., 33:1238–1250, 2015. https://doi.org/10.1186/s13662-015-0379-9.
- D. Baleanu, A.H. Bhrawy and T.M. Taha.: Two efficient generalized Laguerre spectral algorithms for fractional initial value problems. Abstract and Applied Analysis, 2013, 2013.
- D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo. Fractional Calculus. Models and Numerical Methods. World Scientific Publishing Co. Pte. Ltd, Singapore, 2012. https://doi.org/10.1142/8180. doi: 10.1142/8180
- H. Brunner, A. Pedas and G. Vainikko. Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. SIAM J. Numer. Anal., 39(3):957–982, 2001. https://doi.org/10.1137/S0036142900376560.
- R. Čiegis, A. Štikonas, O. Štikoniene and O. Suboč. Stationary problems with nonlocal boundary conditions. Math. Model. Anal., 6, 2001.
- R. Čiegis and N. Tumanova. Numerical solution of parabolic problems with nonlocal boundary conditions. Numer. Funct. Anal. Optim., 31(12): 13181329, 2010. https://doi.org/10.1080/01630563.2010.526734.
- K. Diethelm. The Analysis of Fractional Differential Equations. Springer, Berlin, 2010. https://doi.org/10.1007/978-3-642-14574-2.
- T. Diogo, P.M. Lima, A. Pedas and G. Vainikko. Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations. Appl. Num. Math., 114:63–76, 2017. https://doi.org/10.1016/j.apnum.2016.08.009.
- E.H. Doha, A.H. Bhrawy and S.S. Ezz-Eldien. A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl., 62(5):2364–2373, 2011. https://doi.org/10.1016/j.camwa.2011.07.024.
- N.J. Ford and M.L. Morgado. Fractional boundary value problems: Analysis and numerical methods. Fract. Calc. Appl. Anal., 14(4):554–567, 2011. https://doi.org/10.2478/s13540-011-0034-4.
- N.J. Ford, M.L. Morgado and M. Rebelo. High order numerical methods for fractional terminal value problems. Comput. Methods Appl. Math., 14(1):55–70, 2014. https://doi.org/10.1515/cmam-2013-0022.
- A.A. Kilbas, H.M. Srivastava and J.J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
- M. Kolk and A. Pedas. Numerical solution of Volterra integral equations with weakly singular kernels which may have a boundary singularity. Math. Model. Anal., 14(1):79–89, 2009. https://doi.org/10.3846/1392-6292.2009.14.79-89.
- M. Kolk, A. Pedas and E. Tamme. Modified spline collocation for linear fractional differential equations,. J. Comput. Appl. Math., 283:28–40, 2015. https://doi.org/10.1016/j.cam.2015.01.021.
- I. Parts, A. Pedas and E. Tamme. Piecewise polynomial collocation for Fredholm integro-differential equations with weakly singular kernels. SIAM J. Numer. Anal., 43(5):1897–1911, 2005. https://doi.org/10.1137/040612452.
- A. Pedas and E. Tamme. Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels. J. Comput. Appl. Math., 213(1):111–126, 2008. https://doi.org/10.1016/j.cam.2006.12.024.
- A. Pedas and E. Tamme. On the convergence of spline collocation methods for solving fractional differential equations. J. Comput. Appl. Math., 235(12):3502–3514, 2011. https://doi.org/10.1016/j.cam.2010.10.054.
- A. Pedas and E. Tamme. Piecewise polynomial collocation for linear boundary value problems of fractional differential equations. J. Comput. Appl. Math., 236(13):3349–3359, 2012. https://doi.org/10.1016/j.cam.2012.03.002.
- A. Pedas and E. Tamme. Numerical solution of nonlinear fractional differential equations by spline collocation methods. J. Comput. Appl. Math., 255:216–230, 2014. https://doi.org/10.1016/j.cam.2013.04.049.
- A. Pedas and E. Tamme. Spline collocation for nonlinear fractional boundary value problems. Appl. Math. Comput., 244:502–513, 2014. https://doi.org/10.1016/j.amc.2014.07.016.
- A. Pedas, E. Tamme and M. Vikerpuur. Spline collocation for fractional weakly singular integro-differential equations. Appl. Num. Math., 110:204–214, 2016. https://doi.org/10.1016/j.apnum.2016.07.011.
- A. Pedas, E. Tamme and M. Vikerpuur. Smoothing transformation and spline collocation for nonlinear fractional initial and boundary value problems. J. Comput. Appl. Math., 317:1–16, 2017. https://doi.org/10.1016/j.cam.2016.11.022.
- I. Podlubny. Fractional Differential Equations. Academic Press, San Diego, 1999.
- G. Vainikko. Multidimensional Weakly Singular Integral Equations. Springer, Berlin, 1993. https://doi.org/10.1007/BFb0088979.
- R. Yan, S. Sun, H. Lu and Y. Zhao. Existence of solutions for fractional differential equations with integral boundary conditions. Advances in Difference Equations, 2014(1):25, 2014. https://doi.org/10.1186/1687-1847-2014-25.
- H. Zhou, L. Yang and P. Agarwal. Solvability for fractional p-Laplacian differential equations with multipoint boundary conditions at resonance on infinite interval. J. Appl. Math. Comput., 53:51–76, 2017. https://doi.org/10.1007/s12190-015-0957-8.