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Complex Partial Differential Equations
(Springer, 2025) Aksoy, Ü.; Begehr, H.; Çelebi, A.; Shupeyeva, B.
The Schwarz and iterated Dirichlet boundary-value problems are reported on for the polyanalytic operator in certain plane domains having a harmonic Green function. Hybrid polyharmonic Green functions are reviewed upon which open a variety of boundary-value problems for the polyharmonic operator. This topic is far from being complete. The higher the order of the polyharmonic operator the richer is the theory of related hybrid Green functions: they are constructed by continued convoluting harmonic Green, Neumann, Robin functions also incorporating polyharmonic Green–Almansi functions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
The Existence of Positive Solutions to the Fractional Q-Differential Equations with Integral Boundary Conditions
(Taylor & Francis Inc, 2026) Afshari, Hojjat; Rasouli, Hasan; Ahmadkhanlu, Asghar; Karapinar, Erdal
In this research, we investigate the existence of positive solutions to the fractional q-differential equations under new specified boundary conditions. We employ the alpha-theta-contraction fixed point theorem to analyze our results. Additionally, several examples are provided to illustrate the main results.