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Integral equations and initial value problems for nonlinear differential equations of fractional order

✍ Scribed by Nickolai Kosmatov

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
531 KB
Volume
70
Category
Article
ISSN
0362-546X

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✦ Synopsis

We discuss the solvability of integral equations associated with initial value problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray-Schauder Nonlinear Alternative for several types of initial value problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the "reduction" of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator.

πŸ“œ SIMILAR VOLUMES

Initial value problems for higher-order
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