Browsing by Author "Odibat, Zaid"

Now showing 1 - 6 of 6

A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs
(Wiley, 2019) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, a novel approach, namely, the linearization-based approach of homotopy analysis method, to analytically treat non-linear time-fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution based on a linear approximation of the non-linear problem. A comparative study between the proposed approach and standard homotopy analysis approach is illustrated by solving two examples involving non-linear time-fractional parabolic PDEs. The performed numerical simulations demonstrate that the linearization-based approach reduces the computational complexity and improves the performance of the homotopy analysis method.
A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation
(2023) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS).
New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel
(2023) Baleanu, Dumitru; Baleanu, Dumitru; 56389
This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
Nonlinear dynamics and chaos in fractional differential equations with a new generalized Caputo fractional derivative
(2022) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, novel systems of fractional differential equations involving a new generalized Caputo fractional derivative were proposed. The complex dynamic behavior of these systems was studied by numerical simulation. Nonlinear dynamics and chaos in hybrid fractional order systems were investigated using a predictor–corrector algorithm. In particular, the effect of the new generalized fractional derivative parameters on the dynamics of the proposed systems was discussed. The rich variation obtained from the characteristics of the studied systems recommends the implementation of the new generalized derivative in fractional calculus applications.
Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives
(2020) Baleanu, Dumitru; Baleanu, Dumitru; 56389
We introduce a new generalized Caputo-type fractional derivative which generalizes Caputo fractional derivative. Some characteristics were derived to display the new generalized derivative features. Then, we present an adaptive predictor corrector method for the numerical solution of generalized Caputo-type initial value problems. The proposed algorithm can be considered as a fractional extension of the classical Adams-Bashforth-Moulton method. Dynamic behaviors of some fractional derivative models are numerically discussed. We believe that the presented generalized Caputo-type fractional derivative and the proposed algorithm are expected to be further used to formulate and simulate many generalized Caputo type fractional models. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
On a new modification of the erdélyi–kober fractional derivative
(2021) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdélyi–Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputotype Erdélyi–Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.