An Efficient Approach for Solving Differential Equations in the Frame of a New Fractional Derivative Operator
Nourhane Attia,
Ali Akgül,
Djamila Seba,
Abdelkader Nour,
Manuel De la Sen,
Mustafa Bayram
Affiliations
Nourhane Attia
Ecole Nationale Supérieure des Sciences de la Mer et de l’Aménagement du Littoral, Campus Universitaire de Dely Ibrahim, Bois des Cars, B.P. 19, Alger 16320, Algeria
Ali Akgül
Department of Computer Science and Mathematics, Lebanese American University, Beirut 1102 2801, Lebanon
Djamila Seba
Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Engineer’s Sciences, University M’hamed Bougara of Boumerdes, Boumerdes 35000, Algeria
Abdelkader Nour
Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Engineer’s Sciences, University M’hamed Bougara of Boumerdes, Boumerdes 35000, Algeria
Manuel De la Sen
Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Bizkaia, Spain
Mustafa Bayram
Department of Computer Engineering, Biruni University, Topkapı, Istanbul 34010, Turkey
Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann–Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed method.
