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The exact solutions of the conformable time-fractional modified nonlinear schrodinger equation by the trial equation method and modified trial equation method
(Hindawi, 2022) Aderyani, Safoura Rezaei; Saadati, Reza; Vahidi, Javad; Allahviranloo, Tofigh
Using the trial equation method (TEM) and modified trial equation method (MTEM), firstly, we find the analytical solutions of the conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE), and finally, we present numerical results in tables and charts. © 2022 Safoura Rezaei Aderyani et al.
The existence of a unique solution and stability results with numerical solutions for the fractional hybrid integro-differential equations with Dirichlet boundary conditions
(Springer Science and Business Media Deutschland GmbH, 2024) Eidinejad, Zahra; Saadati, Reza; Vahidi, Javad; Li, Chenkuan; Allahviranloo, Tofigh
In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique. Our main goal is to obtain the best approximation using optimal controllers. After studying the stability, we present the reproducing kernel Hilbert space numerical method to obtain approximate solutions to the equation. We finally conclude with numerical results. © The Author(s) 2024.