Artificial neural network for solving the nonlinear singular fractional differential equations
Saeed Althubiti, M Suresh Kumar, Pranay Goswami, Kranti Kumar
Abstract
This paper proposes an artificial neural network (ANN) architecture for solving nonlinear fractional differential equations. The proposed ANN algorithm is based on a truncated power series expansion to substitute the unknown functions in the equations in this approach. Then, a set of algebraic equations is resolved using the ANN technique in an iterative minimization process. Finally, numerical examples are provided to demonstrate the usefulness of the ANN architectures. The results verify that the suggested ANN architecture achieves high accuracy and good stability.
Topics & Concepts
Artificial neural networkNonlinear systemAlgebraic equationDifferential equationMathematicsSet (abstract data type)Series (stratigraphy)Applied mathematicsPower seriesStability (learning theory)Computer scienceDifferential algebraic equationMinificationAlgorithmMathematical optimizationOrdinary differential equationArtificial intelligenceMathematical analysisMachine learningProgramming languagePaleontologyBiologyQuantum mechanicsPhysicsFractional Differential Equations SolutionsModel Reduction and Neural NetworksAdvanced Control Systems Design