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Analytical Approximate Solutions of (N + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(MDPI AG, 2017) Açan, Ömer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas
In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
A Result On A Pata-Ciric Type Contraction At A Point
(MDPI AG, 2020) Karapınar, Erdal; Fulga, Andreea; Rakoˇcevi´c, Vladimir
In this manuscript, we define a new contraction mapping, Pata-Cirictype contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ciric. We proved that in a complete space, each Pata-Cirictype contraction at a point possesses a fixed point. We express an example to illustrate the observed result.

Matematik Bölümü Yayın Koleksiyonu