scholarly journals On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

Entropy ◽  
2015 ◽  
Vol 17 (2) ◽  
pp. 885-902 ◽  
Author(s):  
Soheil Salahshour ◽  
Ali Ahmadian ◽  
Norazak Senu ◽  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Fractional Differential ◽  
Basset Problem

Free Oscillation Solution for Fractional Differential System

2019 ◽  
Vol 14 (12) ◽  
Author(s):  
Masataka Fukunaga
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Indirect Evidence ◽  
Turing Instability ◽  
Mode Analysis ◽  
Free Standing ◽  
Special Cases ◽  
Fractional Differential

Abstract There is a type of fractional differential equation that admits asymptotically free standing oscillations (Fukunaga, M., 2019, “Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations,” ASME J. Comput. Nonlinear Dyn., 14, p. 061005). In this paper, analytical solutions to fractional differential equation for free oscillations are derived for special cases. These analytical solutions are direct evidence for asymptotically standing oscillations, while numerical solutions give indirect evidence.

scholarly journals Least Squares Differential Quadrature Method for the Generalized Bagley–Torvik Fractional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu ◽  
Mădălina Sofia Paşca ◽  
Dumitru Ţucu ◽  
Marioara Lăpădat
Keyword(s):  
Differential Equation ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Differential Quadrature Method ◽  
Accurate Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Approximate Analytical Solutions ◽  
Fractional Differential

In this paper, the least squares differential quadrature method for computing approximate analytical solutions for the generalized Bagley–Torvik fractional differential equation is presented. This new method is introduced as a straightforward and accurate method, fact proved by the examples included, containing a comparison with previous results obtained by using other methods.

Explicit analytical solutions of incommensurate fractional differential equation systems

2021 ◽  
Vol 390 ◽  
pp. 125590
Author(s):  
Ismail T. Huseynov ◽  
Arzu Ahmadova ◽  
Arran Fernandez ◽  
Nazim I. Mahmudov
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Fractional Differential

scholarly journals Analytical solutions for conformable fractional Bratu-type equations

2018 ◽  
Vol 7 (1) ◽  
pp. 15 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Conformable Fractional Derivative ◽  
Fractional Differential

Solving fractional differential equations have a prominent function in different science such as physics and engineering. Therefore, are different definitions of the fractional derivative presented in recent years. The aim of the current paper is to solve the fractional differential equation by a semi-analytical method based on conformable fractional derivative. Fractional Bratu-type equations have been solved by the method and to show its capabilities. The obtained results have been compared with the exact solution.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

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