Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation
Asian Research Journal of Mathematics,
Page 30-43
DOI:
10.9734/arjom/2021/v17i830321
Abstract
In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.
Keywords:
- Nonlocal cauchy problem
- existence
- uniqueness
- error analysis
- Adomian method
- Picard method
How to Cite
Ziada, E. A. A. (2021). Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation. Asian Research Journal of Mathematics, 17(8), 30-43. https://doi.org/10.9734/arjom/2021/v17i830321
References
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EGatsori SK, Ntouyas and Scas YG. On a nonlocal cauchy problem for dierential inclusions. Abstract and Applied Analysis. 2004;425-434.
Guerekata GMA. Cauchy problem for some fractional abstract dierential equation with non local conditions. Nonlinear Analysis. 2009;70:1873-1876.
Hamani SS, Benchora M, Graef JR. Existence results for boundary-value problems with nonlinear fractional dirential inclusions and integral conditions. EJQTDE. 2010;20:1-16.
Aykut A, Yildiz B. On a boundary value problem for a dierential equation with variant retarded argument. Applied Mathematics and Computation. 1998;93:63-71.
Seda _I Gret Araz, Arzu Aykut. On approximate solution of a boundary value problem with retarded argument. Erzincan University Journal of Science and Technology. 2014;7:93-103.
Adomian G. Solving frontier problems of physics: The decomposition method, Kluwer; 1995.
Adomian G. Stochastic system, academic press; 1983.
Adomian G. Nonlinear stochastic operator equations, Academic Press, San Diego; 1986.
Adomian G. Nonlinear stochastic systems: Theory and Applications to Physics, Kluwer; 1989.
Abbaoui K, Cherruault Y. Convergence of Adomian's method applied to dierential equations. Computers Math. Applic. 1994;28:103-109.
Cherruault Y, Adomian G, Abbaoui K, Rach R. Further remarks on convergence of decomposition method. International J. of Bio-Medical Computing. 1995;38:89-93.
Shawaghfeh NT. Analytical approximate solution for nonlinear fractional dierential equations. J. Appl. Math. Comput. 2002;131:517-529.
El-kalla I L. Convergence of the Adomian method applied to a class of nonlinear integral equations. Applied Mathematics Letters. 2008;21:372-376.
Boucherif A. First-order dierential inclusions with nonlocal initial conditions. Applied Mathematics Letters. 2002;15:409-414.
Boucherif A. Nonlocal Cauchy problems for rst-order multivalued dierential equations, Electronic Journal of Dierential Equations. 2002;47:1-9.
Boucherif A, Precup R. On the nonlocal initial value problem for rst order dierential equations. Fixed Point Theory. 2003;4(2):205-212.
Boucherif A. Semilinear evolution inclusions with nonlocal conditions. Applied Mathematics Letters. 2009;22:1145-1149.
Benchohra M, Gatsori EP, Ntouyas SK. Existence results for seme-linear integrodierential inclusions with nonlocal conditions. Rocky Mountain J. Mat. 2004;34:3. Fall
Benchohra M, Hamani S, Ntouyas S. Boundary value problems for dierential equations with fractional order and nonlocal conditions. Nonlinear Analysis. 2009;71:2391-2396.
Deimling K. Nonlinear functional analysis. Springer-Verlag; 1985.
Dugundji J, Granas A. Fixed Point Theory, Monograe Mathematyczne, PWN, Warsaw; 1982.
El-Sayed AMA, Sh. A. Abd El-Salam. On the stability of a fractional order dierential equation with nonlocal initial condtion. EJQTDE. 2008;9(29):1-8.
El-Sayed AMA, Bin-Taher EO. A nonlocal problem of an arbitrary (fractional) orders dierential equation. Alexandria J. of Math. 2010;1(2):59-62.
EGatsori SK, Ntouyas and Scas YG. On a nonlocal cauchy problem for dierential inclusions. Abstract and Applied Analysis. 2004;425-434.
Guerekata GMA. Cauchy problem for some fractional abstract dierential equation with non local conditions. Nonlinear Analysis. 2009;70:1873-1876.
Hamani SS, Benchora M, Graef JR. Existence results for boundary-value problems with nonlinear fractional dirential inclusions and integral conditions. EJQTDE. 2010;20:1-16.
Aykut A, Yildiz B. On a boundary value problem for a dierential equation with variant retarded argument. Applied Mathematics and Computation. 1998;93:63-71.
Seda _I Gret Araz, Arzu Aykut. On approximate solution of a boundary value problem with retarded argument. Erzincan University Journal of Science and Technology. 2014;7:93-103.
Adomian G. Solving frontier problems of physics: The decomposition method, Kluwer; 1995.
Adomian G. Stochastic system, academic press; 1983.
Adomian G. Nonlinear stochastic operator equations, Academic Press, San Diego; 1986.
Adomian G. Nonlinear stochastic systems: Theory and Applications to Physics, Kluwer; 1989.
Abbaoui K, Cherruault Y. Convergence of Adomian's method applied to dierential equations. Computers Math. Applic. 1994;28:103-109.
Cherruault Y, Adomian G, Abbaoui K, Rach R. Further remarks on convergence of decomposition method. International J. of Bio-Medical Computing. 1995;38:89-93.
Shawaghfeh NT. Analytical approximate solution for nonlinear fractional dierential equations. J. Appl. Math. Comput. 2002;131:517-529.
El-kalla I L. Convergence of the Adomian method applied to a class of nonlinear integral equations. Applied Mathematics Letters. 2008;21:372-376.
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