NUMERICAL SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS VIA LAPLACE TRANSFORM
Abstract
In this study, solutions of time-space fractional partial differential equations
(FPDEs) are obtained by utilizing the Shehu transform iterative method. The utility
of the technique is shown by getting numerical solutions to a large number of FPDEs.
Keywords
Full Text:
PDFReferences
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo: Theory and applications
of fractional differential equations, Elsevier, Amsterdam, 2006.
I. Podlubny: Fractional differential equation, Academic Press, San Diego, CA, 1999.
J. Sabatier, O.P. Agarwal, and A.T. Machado: Advances in fractional
calculus: theoretical developments and applications in physics and engineering, Springer, Dordrecht, 2007.
S.G. Samko, A.A. Kilbas, and O.I Marichev: Fractional integrals and derivatives theory and applications, Gordon and Breach, Amsterdam, 1993.
S. Cetinkaya, A. Demir and H. Kodal Sevindir: The analytic solution of initial boundary value problem including time-fractional diffusion equa-
tion. Facta Universitatis Ser. Math. Inform 35 1 (2020), 243-252. DOI Number:https://doi.org/10.22190/FUMI2001243C.
S. Cetinkaya, A. Demir and H. Kodal Sevindir: The analytic solution
of sequential space-time fractional diffusion equation including periodic boundary
conditions. Journal of Mathematical Analysis 11 1 (2020), 17-26.
S. Cetinkaya and A. Demir: The Analytic Solution of Time-Space Frac-
tional Diffusion Equation via New Inner Product with Weighted Function.
Communications in Mathematics and Applications, 10 4 (2019), 865-873,
DOI:http://dx.doi.org/10.26713
S. Cetinkaya, A. Demir and H. Kodal Sevindir: The Analytic Solution
of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation. Communications in Mathematics and Applications 11 1 2020, 173-179, DOI: 10.26713/cma.v11i1.1293
K.V. Zhukovsky and H.M. Srivastava: Analytical solutions for heat diffusion beyond Fourier law. Applied Mathematics and Computation 293 (2017), 423-437.
L. Mahto, S. Abbas, M. Hafayed and H.M. Srivastava: Approximate
Controllability of Sub-Diusion Equation with Impulsive Condition. Mathematics 7 190 (2019), 1-16.
X.J. Yang, H.M. Srivastava, D.F.M. Torres and A. Debbouche: Gen-
eral Fractional-order Anomalous Diffusion with Non-singuler Power-Law Kernel. Thermal Science 21 1 (2017), 1-9.
I. Podlubny: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Dierential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, New York, 1998.
L. Debnath and D.D. Bhatta: Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics. Fract. Calc. Appl. Anal. 7 1 (2018), 21-36.
S. Maitama and W. Zhao: New Integral Transform Shehu Transform a Generalization of Sumudu and Laplace Trans. for Solving Dif. Eqs.. International Journal of Analysis and Applications 17 2 (2019), 167-190.
R. Belgacem, D. Baleanu and A. Bokhari: Shehu Transform and applications to Caputo-fractional differential equations. International Journal of Analysis and Applications, 17 6 (2019), 917-927, DOI: 10.28924/2291-8639-17-2019-917
V. Daftardar-Gejji and H. Jafari: An iterative method for solving nonlinear functional equations. J. Math. Anal. Appl. 316 2 (2006), 753--763.
S. Bhalekar and V. Daftardar-Gejji: Convergence of the new
iterative method. International Journal of Differential Equations (2011),
DOI:10.1155/2011/989065
S. Choudhary and V. Daftardar-Gejji: Invariant subspace method: a tool for solving fractional partial differential equations. Fract. Calc. Appl. Anal. 20 2 (2017), 477{493.
DOI: https://doi.org/10.22190/FUMI200428019C
Refbacks
ISSN 0352-9665 (Print)