Shehu transform on time-fractional Schrodinger equations - an analytical approach

被引:5
作者
Kapoor, Mamta [1 ]
机构
[1] Lovely Profess Univ, Dept Math, Phagwara 144411, Punjab, India
关键词
2D plot; 3D plot; analytical solution; Caputo fractional derivative; Shehu transform; time-fractional Schrodinger equation (1D; 2D; 3D); LAPLACE; SUMUDU;
D O I
10.1515/ijnsns-2021-0423
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In the present study, time-fractional Schrodinger equations are dealt with for the analytical solution using an integral transform named Shehu Transform. Three kinds of time-fractional Schrodinger equations are discussed in the present study. Shehu transform is utilized to reduce the time-fractional PDE along with the fractional derivative in the Caputo sense. The present method is easy to implement in the search for an analytical solution. As no discretization or numerical program is required, the present scheme will surely be helpful in finding the analytical solution to some complex-natured fractional PDEs.
引用
收藏
页码:1981 / 2010
页数:30
相关论文
共 43 条
[31]  
Oldham K., 1974, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order
[32]  
Ortigueira M.D., 2011, FRACTIONAL CALCULUS, DOI [10.1007/978-94-007-0747-4, DOI 10.1007/978-94-007-0747-4]
[33]  
Papouli A., 1957, QAPPL MATH, V14, P405, DOI 10.1090/qam/82734
[34]  
Podlubny I., 1998, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
[35]  
Rawashdeh M.S., 2014, Int. J. Pure Appl. Math, V92, P757, DOI DOI 10.12732/IJPAM.V92I5.10
[36]   On the solution of the fractional nonlinear Schrodinger equation [J].
Rida, S. Z. ;
EI-Sherbiny, H. M. ;
Arafa, A. A. M. .
PHYSICS LETTERS A, 2008, 372 (05) :553-558
[37]   Computational solution of a fractional generalization of the Schrodinger equation occurring in quantum mechanics [J].
Saxena, R. K. ;
Saxena, Ravi ;
Kalla, S. L. .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (05) :1412-1417
[38]   On spectral numerical method for variable-order partial differential equations [J].
Shah, Kamal ;
Naz, Hafsa ;
Sarwar, Muhammad ;
Abdeljawad, Thabet .
AIMS MATHEMATICS, 2022, 7 (06) :10422-10438
[39]   On a generalization of Mittag-Leffler function and its properties [J].
Shukla, A. K. ;
Prajapati, J. C. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (02) :797-811
[40]   Fractional Schrodinger equations with potential and optimal controls [J].
Wang, JinRong ;
Zhou, Yong ;
Wei, Wei .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (06) :2755-2766