A Picard-Thianwan hybrid iterative scheme is proposed for approximating fixed points of contraction mappings in Banach spaces. Convergence and stability results are established for contraction mappings. A rigorous comparison shows that the proposed method converges faster than the Picard, Mann, Ishikawa, Thianwan, Picard--Mann, and Picard--Ishikawa iterations. Extensive numerical experiments for linear and nonlinear contraction mappings, including two-dimensional graphical illustrations, confirm the theoretical findings. In addition, a data-dependence result for approximation operators is derived using the proposed technique. The practical effectiveness of the method is further illustrated by its successful application to Caputo-type fractional differential equations with boundary conditions.
kaneez, S., Alam, A. & Ali, F. (2026). A New Fixed-Point Iteration for Contraction Operators with Applications to Fractional Differential Equations. (e743118). Mathematics and Computational Sciences, (), e743118 https://doi.org/10.30511/mcs.2026.2086068.1759
MLA
kaneez, S., Alam, A., & Ali, F. "A New Fixed-Point Iteration for Contraction Operators with Applications to Fractional Differential Equations" .e743118 , Mathematics and Computational Sciences, , 2026, e743118. doi: 10.30511/mcs.2026.2086068.1759
HARVARD
kaneez, S., Alam, A., & Ali, F. (2026). 'A New Fixed-Point Iteration for Contraction Operators with Applications to Fractional Differential Equations', Mathematics and Computational Sciences, (), e743118. doi: 10.30511/mcs.2026.2086068.1759
CHICAGO
kaneez, S., Alam, A. & Ali, F., "A New Fixed-Point Iteration for Contraction Operators with Applications to Fractional Differential Equations." Mathematics and Computational Sciences, (2026): e743118, doi: 10.30511/mcs.2026.2086068.1759
VANCOUVER
kaneez S., Alam A., Ali F. A New Fixed-Point Iteration for Contraction Operators with Applications to Fractional Differential Equations. MCS. 2026;():e743118. doi: 10.30511/mcs.2026.2086068.1759
