Generalized iterative method for the solution of linear and nonlinear fractional differential equations with composite fractional derivative operator

Krunal B. Kachhia; Jyotindra C. Prajapati; Krunal B. Kachhia; Jyotindra C. Prajapati

doi:10.3934/math.2020186

AIMS Mathematics

2020, Volume 5, Issue 4: 2888-2898. doi: 10.3934/math.2020186

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Research article

Generalized iterative method for the solution of linear and nonlinear fractional differential equations with composite fractional derivative operator

Krunal B. Kachhia ¹,
Jyotindra C. Prajapati ^{2
,
,}

1.
Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Anand-388421, Gujarat, India
2.
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India

Received: 15 October 2019 Accepted: 25 February 2020 Published: 18 March 2020
MSC : Primary: 34A08, 35R11, 26A33; Secondary: 65J15

In present paper, we introduced generalized iterative method to solve linear and nonlinear fractional differential equations with composite fractional derivative operator. Linear/nonlinear fractional diffusion-wave equations, time-fractional diffusion equation, time fractional Navier-Stokes equation have been solved by using generalized iterative method. The graphical representations of the approximate analytical solutions of the fractional differential equations were provided.
- composite fractional derivative,
- fractional diffusion-wave equation,
- Navier-Stokes equation,
- fractional Schrödinger equation,
- Mittag-Leffler function
Citation: Krunal B. Kachhia, Jyotindra C. Prajapati. Generalized iterative method for the solution of linear and nonlinear fractional differential equations with composite fractional derivative operator[J]. AIMS Mathematics, 2020, 5(4): 2888-2898. doi: 10.3934/math.2020186

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Abstract

In present paper, we introduced generalized iterative method to solve linear and nonlinear fractional differential equations with composite fractional derivative operator. Linear/nonlinear fractional diffusion-wave equations, time-fractional diffusion equation, time fractional Navier-Stokes equation have been solved by using generalized iterative method. The graphical representations of the approximate analytical solutions of the fractional differential equations were provided.

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