Existence of the mild solutions for nonlocal fractional differential equations of Sobolev type with iterated deviating arguments

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Abstract

This paper investigates a nonlocal differential equation of Sobolev type of fractional order with iterated deviating arguments in Banach space. The sufficient condition for providing the existence of mild solution to the nonlocal Sobolevtype fractional differential equation with iterated deviating arguments is obtained via technique of fixed-point theorems and analytic semigroup method. Finally, an example is given to explain the applicability of the abstract results developed.

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Chadha, A., & Pandey, D. N. (2016). Existence of the mild solutions for nonlocal fractional differential equations of Sobolev type with iterated deviating arguments. In Springer Proceedings in Mathematics and Statistics (Vol. 164, pp. 25–37). Springer New York LLC. https://doi.org/10.1007/978-3-319-32857-7_3

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