Browsing by Author "Ismail, F."

Now showing 1 - 4 of 4

Citation - WoS: 35
Citation - Scopus: 44
A fractional derivative with non-singular kernel for interval-valued functions under uncertainty
(Elsevier Gmbh, Urban & Fischer verlag, 2017) Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; 56389; Matematik
The purpose of the current investigation is to generalize the concept of fractional derivative in the sense of Caputo Fabrizio derivative (CF-derivative) for interval-valued function under uncertainty. The reason to choose this new approach is originated from the non singularity property of the kernel that is critical to interpret the memory aftermath of the system, which was not precisely illustrated in the previous definitions. We study the properties of CF-derivative for interval-valued functions under generalized Hukuhara-differentiability. Then, the fractional differential equations under this notion are presented in details. We also study three real-world systems such as the falling body problem, Basset and Decay problem under interval-valued CF-differentiability. Our cases involve a demonstration that this new notion is accurately applicable for the mechanical and viscoelastic models based on the interval CF-derivative equations. (C) 2016 Elsevier GmbH. All rights reserved.
Citation - WoS: 30
Citation - Scopus: 41
A novel approach to approximate fractional derivative with uncertain conditions
(Pergamon-elsevier Science Ltd, 2017) Ahmadian, A.; Salahshour, S.; Ali-Akbari, M.; Ismail, F.; Baleanu, D.; 56389; Matematik
This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme. (C) 2017 Published by Elsevier Ltd.
Citation - WoS: 13
Citation - Scopus: 15
An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations
(Wiley-hindawi, 2017) Bishehniasar, M.; Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; 56389; Matematik
The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.
Citation - WoS: 87
Citation - Scopus: 98
Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution
(Elsevier Science Bv, 2017) Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.; 56389; Matematik
The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed. (C) 2017 Elsevier B.V. All rights reserved.