NUMERICAL TREATMENT OF CERTAIN NONLINEAR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS
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Date
2026
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Abstract
Fractional calculus is defined as an extension of classical integration and differ
entiation. On the other side, fractional ordinary or partial differential equations are
used to model a lot of physical problems. In this work, a goal is try for solving some
nonlinear fractional ordinary and partial differential equations using the optimized
decomposition method (ODM), based on the Caputo fractional derivative. This
technique relies on constructing an efficient approximate series that allows obtain
ing relatively accurate solutions without significant computational complexity. The
proposed methodology is applied to a set of numerical examples. The obtained re
sults show a effectiveness, accuracy, and good agreement with the exact solutions.In
addition, from the numerical analysis results, it can be concluded that the pro
posed method is efficient and sufficiently suitable for handling nonlinear fractional
differential equations.