Existence of Iterative Cauchy Fractional Differential Equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32870
Existence of Iterative Cauchy Fractional Differential Equation

Authors: Rabha W. Ibrahim

Abstract:

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

Keywords: Fractional calculus, fractional differential equation, Cauchy equation, Riemann-Liouville fractional operators, Volterra integral equation, non-expansive mapping, iterative differential equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088268

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2647

References:


[1] R. Lewandowski, B. Chorazyczewski, Identification of the parameters of the KelvinVoigt and the Maxwell fractional models, used to modeling of viscoelastic dampers, Computers and Structures 88 (2010) 1-17.
[2] F. Yu, Integrable coupling system of fractional soliton equation hierarchy, Physics Letters A 373 (2009) 3730-3733.
[3] K. Diethelm, N. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002) 229-248.
[4] R. W. Ibrahim , S. Momani, On the existence and uniqueness of solutions of a class of fractional differential equations, J. Math. Anal. Appl. 334 (2007) 1-10.
[5] S. M. Momani, R. W. Ibrahim, On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras, J. Math. Anal. Appl. 339 (2008) 1210-1219.
[6] B. Bonilla , M. Rivero, J. J. Trujillo, On systems of linear fractional differential equations with constant coefficients, App. Math. Comp. 187 (2007) 68-78.
[7] I. Podlubny, Fractional Differential Equations, Acad. Press, London, 1999.
[8] S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl. 252 (2000) 804-812.
[9] R. W. Ibrahim, M. Darus, Subordination and superordination for analytic functions involving fractional integral operator, Complex Variables and Elliptic Equations, 53 (2008) 1021-1031.
[10] R. W. Ibrahim, M. Darus, Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl. 345 (2008) 871-879.
[11] R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives, J. Phys. Chem. Bio. 104(2000) 3914-3917.
[12] R. W. Ibrahim, Existence and uniqueness of holomorphic solutions for fractional Cauchy problem, J. Math. Anal. Appl. 380 (2011) 232-240.
[13] A. A. Kilbas, H. M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations. North-Holland, Mathematics Studies, Elsevier 2006.
[14] V. Berinde, Iterative Approximation of Fixed Points,2nd Ed.,Springer Verlag, Berlin Heidelberg New York, 2007.
[15] M. Edelstein, A remark on a theorem of M. A. Krasnoselskij, Amer. Math. Monthly, 73(1966) 509-510.
[16] E. Egri, I. Rus, First order iterative functional-dierential equation with parameter, Stud. Univ. Babes-Bolyai Math. 52 (2007) 67-80.
[17] C. Chidume, Geometric Properties of Banach spaces and nonlinear Iterations, Springer Verlag, Berlin, Heidelberg, New York, 2009.
[18] Yang, D. and Zhang, W., Solution of equivariance for iterative differential equations, Appl. Math. Lett. 17(2004) 759-765.
[19] A. Ronto, M. Ronto, Succsesive approximation method for some linear boundary value problems for differential equations with a special type of argument deviation, Miskolc Math. Notes, 10(2009) 69-95.
[20] V. Berinde, Existence and approximation of solutions of some first order iterative differential equations, Miskolc Math. Notes,Vol. 11 (2010) pp. 1326.