@article{(Open Science Index):https://publications.waset.org/pdf/16803,
	  title     = {Stability of Fractional Differential Equation},
	  author    = {Rabha W. Ibrahim},
	  country	= {},
	  institution	= {},
	  abstract     = {We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {7},
	  number    = {3},
	  year      = {2013},
	  pages     = {487 - 492},
	  ee        = {https://publications.waset.org/pdf/16803},
	  url   	= {https://publications.waset.org/vol/75},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 75, 2013},
	}