Operational Methods For Sub - Ballistic And Coupled Fractional PDEs

Arman Aghili [1]

28 25

In this article, it is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve a certain system of fractional PDEs and a variety of Lamb - Bateman singular integral equation. The Lamb - Bateman singular integral equation was introduced to study the solitary wave diffraction. It may be concluded that the integral transforms and exponential operators are effective methods for solving integral equations and fractional linear equations with non-constant coefficients.

Fractional partial differential equations, Exponential operational method, Riemann - Liouville fractional derivative, Laplace transform, Caputo fractional derivative, Fourier transform
  • [1] 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.
  • [2] A. Aghili, Fractional Black - Scholes equation, International Journal of Financial Engineering, 4(1), (2017) 1750004 (15 pages)© World Scientific Publishing Company.
  • [3] A.Aghili, H.Zeinali: New Trends In Laplace Type Integral Transforms With Applications. Bol. Soc. Paran. Mat. Vol. 35,1. (2017), 174 - 191.
  • [4] A.Apelblat. Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
  • [5] D.Babusci, G.Dattoli, D.Sacchetti. The Lamb - Bateman integral equation and the fractional derivatives.Fractional calculus and applied analysis.vol 14, no 2, 2011.pp 317 - 320.
  • [6] G.Dattoli. Operational methods, fractional perators and special polynomials. Applied Mathematics and computations.141 (2003) pp 151-159.
  • [7] 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.
  • [8] I. Podlubny. Fractional Differential Equations, Academic Press, San Diego, CA,1999.
  • [9] F.Usta, H.Budak, M.Z.Sarikaya, Yang - Laplace transform method for local fractional Volterra and Abel’s integro - differential equations. www.reaearchgate.net/publication/316923150.
  • [10] F.Usta, Numerical solution of fractional elliptic PDEs by collocation method, Appl. Appl. Math.,2017,12(1), 470 - 478.
  • [11] X.Y. Yang, D.Baleanu, H.M.Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press,Amesterdam,(2016).
Birincil Dil en
Konular Mühendislik ve Temel Bilimler
Dergi Bölümü Articles
Yazarlar

Yazar: Arman Aghili
E-posta: arman.aghili@gmail.com
Ülke: Iran


Bibtex @araştırma makalesi { konuralpjournalmath417631, journal = {Konuralp Journal of Mathematics}, issn = {}, address = {Mehmet Zeki SARIKAYA}, year = {}, volume = {6}, pages = {42 - 48}, doi = {}, title = {Operational Methods For Sub - Ballistic And Coupled Fractional PDEs}, key = {cite}, author = {Aghili, Arman} }
APA Aghili, A . (). Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp Journal of Mathematics, 6 (1), 42-48. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/417631
MLA Aghili, A . "Operational Methods For Sub - Ballistic And Coupled Fractional PDEs". Konuralp Journal of Mathematics 6 (): 42-48 <http://dergipark.gov.tr/konuralpjournalmath/issue/31478/417631>
Chicago Aghili, A . "Operational Methods For Sub - Ballistic And Coupled Fractional PDEs". Konuralp Journal of Mathematics 6 (): 42-48
RIS TY - JOUR T1 - Operational Methods For Sub - Ballistic And Coupled Fractional PDEs AU - Arman Aghili Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 42 EP - 48 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2018 ER -
EndNote %0 Konuralp Journal of Mathematics Operational Methods For Sub - Ballistic And Coupled Fractional PDEs %A Arman Aghili %T Operational Methods For Sub - Ballistic And Coupled Fractional PDEs %D 2018 %J Konuralp Journal of Mathematics %P -2147-625X %V 6 %N 1 %R %U