scholarly journals Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1037 ◽  
Author(s):  
Jehad Alzabut ◽  
James Viji ◽  
Velu Muthulakshmi ◽  
Weerawat Sudsutad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Oscillatory Behavior ◽  
Numerical Examples ◽  
Oscillation Criteria ◽  
Fractional Differential

In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

A Robust Computational Algorithm of Homotopy Asymptotic Method for Solving Systems of Fractional Differential Equations

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zaid Odibat ◽  
Sunil Kumar
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Asymptotic Method ◽  
Computational Algorithm ◽  
Series Solutions ◽  
Numerical Examples ◽  
Convergence Of Series ◽  
New Ideas ◽  
Fractional Differential ◽  
Optimal Construction

In this paper, we present new ideas for the implementation of homotopy asymptotic method (HAM) to solve systems of nonlinear fractional differential equations (FDEs). An effective computational algorithm, which is based on Taylor series approximations of the nonlinear equations, is introduced to accelerate the convergence of series solutions. The proposed algorithm suggests a new optimal construction of the homotopy that reduces the computational complexity and improves the performance of the method. Some numerical examples are tested to validate and illustrate the efficiency of the proposed algorithm. The obtained results demonstrate the improvement of the accuracy by the new algorithm.

scholarly journals A New Scheme for Solving Multiorder Fractional Differential Equations Based on Müntz–Legendre Wavelets

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
Pseudospectral Method ◽  
Algebraic Equations ◽  
Legendre Wavelets ◽  
Derivative Operator ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
Fractional Differential

In this study, we apply the pseudospectral method based on Müntz–Legendre wavelets to solve the multiorder fractional differential equations with Caputo fractional derivative. Using the operational matrix for the Caputo derivative operator and applying the Chebyshev and Legendre zeros, the problem is reduced to a system of linear algebraic equations. We illustrate the reliability, efficiency, and accuracy of the method by some numerical examples. We also compare the proposed method with others and show that the proposed method gives better results.

scholarly journals Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Nonlinear Fractional Differential Equations ◽  
Inequality Technique ◽  
Fractional Differential ◽  
Oscillation Of Solutions

We are concerned with oscillation of solutions of a class of nonlinear fractional differential equations with damping term. Based on a generalized Riccati function and inequality technique, we establish some new oscillation criteria for it. Some applications are also presented for the established results.

scholarly journals Interval Oscillation Criteria for a Class of Fractional Differential Equations with Damping Term

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chunxia Qi ◽  
Junmo Cheng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Transformation ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Interval Oscillation ◽  
Inequality Technique ◽  
Fractional Differential

Some new interval oscillation criteria are established based onthe certain Riccati transformation and inequality techniquefor a class of fractional differential equations with damping term. For illustrating the validity of the established results, we also present some applications for them.

scholarly journals General solution of Bernoulli and Riccati fractional differential equations based on conformable fractional derivative

2017 ◽  
Vol 6 (2) ◽  
pp. 49 ◽  
Author(s):  
Zainab Ayati ◽  
Jafar Biaar ◽  
Mousa Ilei
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Conformable Fractional Derivative ◽  
Numerical Examples ◽  
Fractional Differential

This paper is aimed to develop two well-known nonlinear ordinary differential equations, Bernoulli and Riccati equations to fractional form. General solution to fractional differential equations are detected, based on conformable fractional derivative. For each equation, numerical examples are presented to illustrate the proposed approach.  

scholarly journals A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2166
Author(s):  
Tofigh Allahviranloo ◽  
Zahra Noeiaghdam ◽  
Samad Noeiaghdam ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Taylor Expansion ◽  
Direct Method ◽  
Numerical Examples ◽  
Euler’S Method ◽  
Truncation Errors ◽  
Fractional Differential ◽  
Fuzzy Fractional Differential Equations

In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method.

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