A Residual Power Series Technique for Solving Systems of Initial Value Problems

2016 ◽  
Vol 10 (2) ◽  
pp. 765-775 ◽  
Author(s):  
Shaher Momani ◽  
Omar Abu Arqub ◽  
Ma’mon Abu Hammad ◽  
Zaer S. Abo-Hammour
Keyword(s):  
Power Series ◽  
Initial Value Problems ◽  
Initial Value ◽  
Residual Power Series ◽  
Power Series Technique ◽  
Residual Power ◽  
Series Technique

scholarly journals Analytical solutions forfuzzysystem using power series approach

2016 ◽  
Vol 12 (8) ◽  
pp. 6553-6559
Author(s):  
Sana Abughurra
Keyword(s):  
Power Series ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Convergent Series ◽  
Initial Value ◽  
Generalized Differentiability ◽  
Residual Power Series ◽  
Strongly Generalized Differentiability ◽  
Fuzzy Equations ◽  
Residual Power

The aim of the present paper is present a relatively new analytical method, called residual power series (RPS) method, for solving system of fuzzy initial value problems under strongly generalized differentiability. The technique methodology provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. The results reveal that the present simulated method is very effective, straightforward and powerful methodology to solve such fuzzy equations.

scholarly journals Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1646
Author(s):  
Malik Bataineh ◽  
Mohammad Alaroud ◽  
Shrideh Al-Omari ◽  
Praveen Agarwal
Keyword(s):  
Applied Sciences ◽  
Power Series ◽  
Differential Equations ◽  
Fractional Power ◽  
Approximate Solutions ◽  
Residual Power Series ◽  
Comparative Results ◽  
Physical Phenomena ◽  
Power Series Technique ◽  
Residual Power

Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena.

scholarly journals Adaptation of Conformable Residual Power Series Scheme in Solving Nonlinear Fractional Quantum Mechanics Problems

2020 ◽  
Vol 10 (3) ◽  
pp. 890 ◽  
Author(s):  
Mohammed Shqair ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Essam El-Zahar
Keyword(s):  
Quantum Mechanics ◽  
Power Series ◽  
Quantum Physics ◽  
Taylor Series Expansion ◽  
Fractional Quantum ◽  
Analytical Technique ◽  
Different Types ◽  
Residual Power Series ◽  
Residual Errors ◽  
Residual Power

In this paper, the general state of quantum mechanics equations that can be typically expressed by nonlinear fractional Schrödinger models will be solved based on an attractive efficient analytical technique, namely the conformable residual power series (CRPS). The fractional derivative is considered in a conformable sense. The desired analytical solution is obtained using conformable Taylor series expansion through substituting a truncated conformable fractional series and minimizing its residual errors to extract a supportive approximate solution in a rapidly convergent fractional series. This adaptation can be implemented as a novel alternative technique to deal with many nonlinear issues occurring in quantum physics. The effectiveness and feasibility of the CRPS procedures are illustrated by verifying three realistic applications. The obtained numerical results and graphical consequences indicate that the suggested method is a convenient and remarkably powerful tool in solving different types of fractional partial differential models.

Sign in / Sign up

Export Citation Format

Share Document