Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space

By Omar Abu Arqub, M. Al‐Smadi. Chaos, Solitons & Fractals, 2018

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Abstract In this analysis, by developed the reproducing kernel Hilbert space method within the Atangana–Baleanu fractional approach, the Bagley–Torvik and Painleve equations are solved with respect to initial conditions of necessity. The solution methodology involves the use of two Hilbert spaces for both range and domain space. Numerical algorithm and procedure of solution are assembled compatibility with the cogent formulation of the problem. The method of solution of the utilized problems is studied under some hypotheses, which provides the theoretical structure behind the technique. The solutions profiles show the performance of the numerical solutions and the effect of the Atangana–Baleanu fractional approach in the obtained results. In this approach, computational simulations are introduced to delineate suitability, straightforwardness, and relevance of the calculations created.

Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/86871a6d6e55a2ad7c6551d0309338fbb64ab946

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In Applied Mathematics

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis (2019, methodology): “Iterative and numeric schemes of the RKHSM have been modified and provided to handle the solutions behaviors by utilizing linear differential operator in Hilbert spaces.(26-48) In the sense of modern theoretical utilization, the pattern of this article is as follows:”