M. Wajiha - Department of Mathematics, The Government Sadiq College Women University, Girls College Road, Anwar Colony, Bahawalpur, 63100, Punjab, Pakistan. I. Talib - Nonlinear Analysis Group, Department of Mathematics, Virtual University of Pakistan, 54-Lawrence Road, Lahore, 54000, Punjab, Pakistan. D. Baleanu - Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. M. S. Hashmi - Department of Mathematics, The Government Sadiq College Women University, Girls College Road, Anwar Colony, Bahawalpur, 63100, Punjab, Pakistan.
In the presented study, we address two-point boundary value problems in the Caputo framework by extending the operational matrices approach. This approach has previously been used in the literature to solve problems modeled with initial conditions. The proposed method relies on newly constructed operational matrices for fractional-order integrals derived from shifted Gegenbauer polynomials. Through the inclusion of monomial terms in the proposed computational scheme, these matrices convert the problem into Sylvester-form matrix equations that can be resolved effectively. Moreover, our approach is applicable to problems admitting either polynomial or non-polynomial solutions. In order to assess the precision and efficiency of our method, we compare its results with those produced by the Bessel Collocation approach, the Haar Wavelet approach, a hybrid approach combining the Homotopy Perturbation approach with Green's function, and the Fractional Central Formula for the Caputo differentiator. This comparative analysis confirms the effectiveness of our approach.
M. Wajiha, I. Talib, D. Baleanu, M. S. Hashmi, Efficient computational framework for solving boundary value problems in Caputo setting with polynomial and non-polynomial solutions, Journal of Mathematics and Computer Science, 41 (2026), no. 4, 437--455
Wajiha M., Talib I., Baleanu D., Hashmi M. S., Efficient computational framework for solving boundary value problems in Caputo setting with polynomial and non-polynomial solutions. J Math Comput SCI-JM. (2026); 41(4):437--455
Wajiha, M., Talib, I., Baleanu, D., Hashmi, M. S.. "Efficient computational framework for solving boundary value problems in Caputo setting with polynomial and non-polynomial solutions." Journal of Mathematics and Computer Science, 41, no. 4 (2026): 437--455
