Local existence theorems for ordinary differential equations of fractional order

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

Download Full-text

F-Expansion Method and Its Application for Finding Exact Analytical Solutions of Fractional order RLW Equation

10.22541/au.162353738.80673939/v1 ◽

2021 ◽

Author(s):

Attia Rani ◽

Qazi Mahmood Ul-Hassan ◽

Muhammad Ashraf ◽

Jamshad Ahmad

Keyword(s):

Solitary Wave ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Fractional Order ◽

Nonlinear Partial Differential Equation ◽

Expansion Method ◽

Nonlinear Evolution Equations ◽

Partial Differential ◽

Wave Solutions ◽

Rlw Equation

Exact nonlinear partial differential equation solutions are critical for describing new complex characteristics in a variety of fields of applied science. The aim of this research is to use the F-expansion method to find the generalized solitary wave solution of the regularized long wave (RLW) equation of fractional order. Fractional partial differential equations can also be transformed into ordinary differential equations using fractional complex transformation and the properties of the modified Riemann–Liouville fractional-order operator. Because of the chain rule and the derivative of composite functions, nonlinear fractional differential equations (NLFDEs) can be converted to ordinary differential equations. We have investigated various set of explicit solutions with some free parameters using this approach. The solitary wave solutions are derived from the moving wave solutions when the parameters are set to special values. Our findings show that this approach is a very active and straightforward way of formulating exact solutions to nonlinear evolution equations that arise in mathematical physics and engineering. It is anticipated that this research will provide insight and knowledge into the implementation of novel methods for solving wave equations.

Download Full-text

Variational Iteration Method for Solving System of Fractional Order Ordinary Differential Equations

IOSR Journal of Mathematics ◽

10.9790/5728-10624854 ◽

2014 ◽

Vol 10 (6) ◽

pp. 48-54

Author(s):

Nabaa N. Hasan ◽

◽

Fadhel S.Fadhel

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Fractional Order ◽

Iteration Method ◽

Variational Iteration Method ◽

Variational Iteration

Download Full-text

A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals ◽

10.1142/s0218348x2050070x ◽

2020 ◽

Vol 28 (04) ◽

pp. 2050070 ◽

Cited By ~ 1

Author(s):

CONG WU

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Ordinary Differential Equations ◽

Fractional Order ◽

Comparison Principle ◽

Caputo Fractional Derivative ◽

Fractional Derivatives ◽

Fractional Order Systems ◽

Caputo Fractional Derivatives ◽

Full Result

In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

Download Full-text