On a new class of impulsive \(\eta\)-Hilfer fractional Volterra-Fredholm integro-differential equations. (English) Zbl 1536.45003
Summary: This work addresses the idea of the uniqueness and existence results for a class of boundary value problems (BVPs) for implicit Volterra-Fredholm integro-differential equations (V-FIDEs) with fractional \(\eta\)-Hilfer nonlinear equations and multi-point fractional boundary non-instantaneous conditions. The conclusions are confirmed by the fixed point of Krasnoselskii’s theorem and the Banach contraction principle. Finally, a concrete example is given to illustrate our main conclusions.
MSC:
| 45J05 | Integro-ordinary differential equations |
| 45D05 | Volterra integral equations |
| 45B05 | Fredholm integral equations |
| 26A33 | Fractional derivatives and integrals |
| 47N20 | Applications of operator theory to differential and integral equations |
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