We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional p-Laplacian (-Δ)psu=f(x,u)-∫Ω|u(y)|r|x-y|αdy|u(x)|r-2u(x)inΩ,u=0inRN\Ω.\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} (-\Delta )_p^su = f(x,u) -\displaystyle \left( \int \limits _\Omega \frac{|u(y)|^r}{|x-y|^\alpha }dy\right) |u(x)|^{r-2}u(x)~\text { in }~ \Omega , ~u=0 ~\text { in }~ {{\mathbb {R}}}^N\setminus \Omega . \end{aligned}$$\end{document}Here Ω⊂RN(N≥2)\documentclass[12pt]{minimal}
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\begin{document}$$ \Omega \subset {{\mathbb {R}}}^N(N\ge 2)$$\end{document} is a bounded domain with C1,1\documentclass[12pt]{minimal}
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\begin{document}$$ C^{1,1}$$\end{document} boundary ∂Ω\documentclass[12pt]{minimal}
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\begin{document}$$\partial \Omega $$\end{document}, s∈(0,1)\documentclass[12pt]{minimal}
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\begin{document}$$ s \in (0,1) $$\end{document}, p∈(1,∞)\documentclass[12pt]{minimal}
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\begin{document}$$p \in (1,\infty )$$\end{document} are such that ps<N\documentclass[12pt]{minimal}
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\begin{document}$$ps < N$$\end{document}. Also ps,α#≤r<∞\documentclass[12pt]{minimal}
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\begin{document}$$p_{s,\alpha }^\#\le r<\infty $$\end{document}, where ps,α#=(2N-α)/2N\documentclass[12pt]{minimal}
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\begin{document}$$p_{s,\alpha }^\#=(2N-\alpha )/2N$$\end{document}. Under suitable and general assumptions on the nonlinearity f, we study the existence, nonexistence, uniqueness, and regularity of weak solutions. As for applications, we treat cases of subdiffusive type logistic Choquard problem. We also consider in the superdiffusive case the Brezis-Nirenberg type problem with logistic Choquard and show the existence of a nontrivial solution for a suitable choice of λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document}. Finally for a particular choice of f viz. f(x,t)=λtq-1\documentclass[12pt]{minimal}
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\begin{document}$$f(x,t)=\lambda t^{q-1}$$\end{document} with 1<p<2r<q\documentclass[12pt]{minimal}
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\begin{document}$$1<p<2r<q$$\end{document}, we show the existence of at least one energy nodal solution.
