Abstract
References
- A.Aghili, H.Zeinali. Advances in Laplace type integral transforms with applications, Indian Journal of Science and Technology, Vol. 7(6), 877-890, June 2014.
- A.Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences. Vol. 3, issue 4, Dec. 2015.pp 133-143.
- A.Ansari. Fractional exponential operators and time fractional telegraph equation. Boundary value problems. 2012, Springer.
- A.Apelblat. Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
- B. Davies. Integral transforms and their applications, Springer, USA, 2001.
- G.Dattoli. Operational methods, fractional operators and special polynomials. Applied Mathematics and computations.141 (2003) pp 151-159.
- G.Dattoli, H.M.Srivastava,K.V.Zhukovsky. Operational methods and differential equations to initial value problems. Applied Mathematics and computations.184 (2007) pp 979-1001.
- G.Dattoli, P.E.Ricci C.Cesarano.L.Vasquez. Mathematical and computer modelling.37 (2003)729-733
- A.A.Kilbas, H.M. Srivastava, J.J.Trujillo, Theory and applications of fractional differential equations, North Holand Mathematics Studies,204,Elsevier Science Publishers ,Amesterdam, Heidelberg and New York ,2006.
- I. Podlubny. Fractional Differential Equations, Academic Press, San Diego, CA,1999.
Abstract
In this article, it is shown that the combined use of
exponential operators and special functions provides a powerful tool to solve
certain type of fractional PDEs. A system of space fractional partial
differential equations is solved. The exponential operators are powerful and
effective method for solving certain singular integral equations and fractional
partial differential equations with non-constant coefficients. Constructive
examples are also provided.
Keywords
Fractional partial differential equations Riemann Liouville fractional derivative Fredholm singular integral equation
References
- A.Aghili, H.Zeinali. Advances in Laplace type integral transforms with applications, Indian Journal of Science and Technology, Vol. 7(6), 877-890, June 2014.
- A.Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences. Vol. 3, issue 4, Dec. 2015.pp 133-143.
- A.Ansari. Fractional exponential operators and time fractional telegraph equation. Boundary value problems. 2012, Springer.
- A.Apelblat. Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
- B. Davies. Integral transforms and their applications, Springer, USA, 2001.
- G.Dattoli. Operational methods, fractional operators and special polynomials. Applied Mathematics and computations.141 (2003) pp 151-159.
- G.Dattoli, H.M.Srivastava,K.V.Zhukovsky. Operational methods and differential equations to initial value problems. Applied Mathematics and computations.184 (2007) pp 979-1001.
- G.Dattoli, P.E.Ricci C.Cesarano.L.Vasquez. Mathematical and computer modelling.37 (2003)729-733
- A.A.Kilbas, H.M. Srivastava, J.J.Trujillo, Theory and applications of fractional differential equations, North Holand Mathematics Studies,204,Elsevier Science Publishers ,Amesterdam, Heidelberg and New York ,2006.
- I. Podlubny. Fractional Differential Equations, Academic Press, San Diego, CA,1999.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2016 |
| IZ | https://izlik.org/JA46YP73AB |
| Published in Issue | Year 2016 Volume: 4 Issue: 4 |