Residual power series method for time-fractional Schrödinger equations

Yu, Ziyou; Kumar, Amit; Kumar, Sunil; Băleanu, Dumitru; Yang, Xiao‐Jun

doi:10.22436/jnsa.009.11.10

Cited by 53 publications

(21 citation statements)

References 15 publications

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“…The combination of different control combinations, cases 1-4 are performed, and we concluded by activating the three controls at the same time can best reduce the number of infective individuals in Pakistan. In future work, we consider analyzing this model involving derivatives and integrals of noninteger order [23][24][25][26][27][28] and compare the results obtained.…”

Section: Resultsmentioning

confidence: 99%

Mathematical formulation of hepatitis B virus with optimal control analysis

Ullah

Khan

Gómez‐Aguilar

2019

Optim Control Appl Methods

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Summary Hepatitis B infection is a serious health issue and causes many deaths around the world. The aim of this paper is to develop a mathematical model with hospitalized population to explore the dynamics of this infection. Initially, we study the model without control and carried out all the basic properties and results including local and global stability. After that, we develop the model with suitable optimal control strategies and explore the necessary optimality conditions using the well known Pontryagin's maximum principle to minimize the spread of hepatitis B in a community. Finally, we present the numerical simulations of both with and without control models to illustrate the feasibility of the control strategy.

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Section: Resultsmentioning

confidence: 99%

Mathematical formulation of hepatitis B virus with optimal control analysis

Ullah

Khan

Gómez‐Aguilar

2019

Optim Control Appl Methods

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“…In this part, we now proceed to discuss the applications of new YAC fractional derivative through HPTM and residual power series method (RPSM). The essential theory of HPTM and RPSM and its utilization to the physical problems are given in published literature …”

Section: Solutions Of Time‐fractional Multidimensional Heat Equationsmentioning

confidence: 99%

“…The RPSM consists in expression the solution of Equation as a multiple FPS expansions about the initial point

t = t_{0}

. Let solution takes the following form.…”

Section: Solutions Of Time‐fractional Multidimensional Heat Equationsmentioning

confidence: 99%

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Kumar

Ghosh

Samet

et al. 2020

Math Methods in App Sciences

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175

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The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multi dimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang-Abdel-Aty-Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag-Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator. KEYWORDS HPTM and RPSM, multidimensional heat equations, new fractional derivative, new YAC operator, Prabhakar or generalized Mittag-Leffler function MSC CLASSIFICATION 26A33; 34A08; 34A34; 60G22 Math Meth Appl Sci. 2020;43:6062-6080. wileyonlinelibrary.com/journal/mma

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“…Recently, due to its consistency and efficacy, it has aided by many researchers to interpret results for various kinds of nonlinear problem, like the authors in [29]; analyze and find the solution for the Biswas-Milovic equation having fractional order; the arbitrary order Schrodinger equation has been profitably analyzed in [30]; the authors in [31] employed it to find the solution for the Fisher equation with fractional order; the applicability and efficiency of RPSM is presented in [32] to solve PDEs; scholars in [33], have analyzed coupled equations arising in fluid flow; and many other are aided by the considered scheme to analyze and find the solution for complex non-linear problems describing complex phenomena.…”

Section: Introductionmentioning

confidence: 99%

Residual Power Series Method for Fractional Swift–Hohenberg Equation

2019

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In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the proposed technique, we consider a non-linear fractional order Swift–Hohenberg equation in the presence and absence of dispersive terms. The effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied and presented through plots. The results obtained show that the proposed technique is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.

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Residual power series method for time-fractional Schrödinger equations

Cited by 53 publications

References 15 publications

Mathematical formulation of hepatitis B virus with optimal control analysis

Mathematical formulation of hepatitis B virus with optimal control analysis

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Residual Power Series Method for Fractional Swift–Hohenberg Equation

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