Semi-analytic solutions of nonlinear multidimensional fractional differential equations
Copyright policy )Semi-analytic solutions of nonlinear multidimensional fractional differential equations
<abstract><p>In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.</p></abstract>
Picard method, Decomposition method (queueing theory), Economics, Bassset problem, Fractional ordinary differential equations, Convolution (computer science), Differential equation, Numerical Methods for Singularly Perturbed Problems, Series (stratigraphy), Numerical Analysis, Ecology, Applied Mathematics, Physics, Discrete mathematics, Fractional Derivatives, adomian decomposition, Modeling and Simulation, Derivative (finance), Physical Sciences, Convergence (economics), Numerical methods for ordinary differential equations, Type (biology), Biotechnology, picard method, Artificial neural network, Financial economics, Fractional Differential Equations, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, caputo-fabrizo, Caputo-Fabrizo, Machine learning, QA1-939, FOS: Mathematics, multidimensional, Functional Differential Equations, Biology, Anomalous Diffusion Modeling and Analysis, Economic growth, Fractional calculus, Pure mathematics, Paleontology, fractional differential equations, Applied mathematics, Computer science, Adomian decomposition, Semilinear Differential Equations, Exact solutions in general relativity, bassset problem, FOS: Biological sciences, Nonlinear system, Kernel (algebra), Fractional Calculus, Adomian decomposition method, TP248.13-248.65, Mathematics
Picard method, Decomposition method (queueing theory), Economics, Bassset problem, Fractional ordinary differential equations, Convolution (computer science), Differential equation, Numerical Methods for Singularly Perturbed Problems, Series (stratigraphy), Numerical Analysis, Ecology, Applied Mathematics, Physics, Discrete mathematics, Fractional Derivatives, adomian decomposition, Modeling and Simulation, Derivative (finance), Physical Sciences, Convergence (economics), Numerical methods for ordinary differential equations, Type (biology), Biotechnology, picard method, Artificial neural network, Financial economics, Fractional Differential Equations, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, caputo-fabrizo, Caputo-Fabrizo, Machine learning, QA1-939, FOS: Mathematics, multidimensional, Functional Differential Equations, Biology, Anomalous Diffusion Modeling and Analysis, Economic growth, Fractional calculus, Pure mathematics, Paleontology, fractional differential equations, Applied mathematics, Computer science, Adomian decomposition, Semilinear Differential Equations, Exact solutions in general relativity, bassset problem, FOS: Biological sciences, Nonlinear system, Kernel (algebra), Fractional Calculus, Adomian decomposition method, TP248.13-248.65, Mathematics
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