# A study of fractional Schrödinger equation composed of Jumarie fractional derivative

@article{Banerjee2016ASO, title={A study of fractional Schr{\"o}dinger equation composed of Jumarie fractional derivative}, author={Joydip Banerjee and Uttam Ghosh and Susmita Sarkar and Shantanu Das}, journal={Pramana}, year={2016}, volume={88}, pages={1-15} }

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in…

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## References

SHOWING 1-10 OF 29 REFERENCES

### Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results

- MathematicsComput. Math. Appl.
- 2006

### Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals

- Mathematics
- 2015

In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type fractional derivative, and describe this method developed by…

### Solution of System of Linear Fractional Differential Equations with Modified derivative of Jumarie Type

- Mathematics
- 2015

Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to…

### An approach to differential geometry of fractional order via modified Riemann-Liouville derivative

- Mathematics
- 2012

In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one (Jumarie)…

### Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag- Leffler Function

- Mathematics
- 2015

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied.…

### Fractional Weierstrass function by application of Jumarie fractional trigonometric functions and its analysis

- Mathematics
- 2015

The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we define the fractional order Weierstrass function in terms of Jumarie…

### The Fractional Sub-Equation Method and Exact Analytical Solutions for Some Nonlinear Fractional PDEs

- Mathematics
- 2013

In the present paper, a fractional sub-equation method is proposed to solve fractional differential equations. Being concise and straightforward, this method is applied the space–time fractional…

### Functional Fractional Calculus

- Mathematics
- 2011

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or…

### On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling

- Mathematics
- 2013

It has been pointed out that the derivative chains rules in fractional differential calculus via fractional calculus are not quite satisfactory as far as they can yield different results which depend…

### Fractal differential equations and fractal-time dynamical systems

- Mathematics
- 2005

AbstractDifferential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous and discrete time-evolution processes respectively. The…