alexa Analysis of nonlinear integral equations with Erdélyi–Kober fractional operator


Journal of Applied & Computational Mathematics

Author(s): JinRong Wang, XiWang Dong, Yong Zhou

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This paper initiates the investigation of nonlinear integral equations with Erdélyi–Kober fractional operator. Existence and uniqueness results of solutions in a closed ball are obtained by using a directly computational method and Schauder fixed point theorem via a weakly singular integral inequality due to Ma and Pec˘arić [20]. Meanwhile, three certain solutions sets YK,σ, Y1,λ and Y1,1, which tending to zero at an appropriate rate t−ν, 0 < ν = σ (or λ or 1) as t → +∞, are constructed and local stability results of solutions are obtained based on these sets respectively under some suitable conditions. Two examples are given to illustrate the results.

This article was published in Communications in Nonlinear Science and Numerical Simulation and referenced in Journal of Applied & Computational Mathematics

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