@article { author = {Mahmoudieh, Mohammad and Hosseinnezhad, Hessam and Abbaspour Tabadkan, Gholamreza}, title = {Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {1-18}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.77908.356}, abstract = {In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multi-frames (resp. multi-Riesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.}, keywords = {Multi-frame vector,Wandering vector,Local commutant,Unitary system}, url = {https://scma.maragheh.ac.ir/article_34968.html}, eprint = {https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf} } @article { author = {Banaei, Shahram and Ghaemi, Mohammad Bagher}, title = {A Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {19-35}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.74869.322}, abstract = {In this paper, we generalize the Meir-Keeler condensing  operators  via a concept of the class of operators  $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems.  As an application of this extension, we  analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally,  we present an example  to show the effectiveness of our results. We use the technique of measure of noncompactness to obtain our results.}, keywords = {Measure of noncompactness,Fixed point theorem,Integral equations}, url = {https://scma.maragheh.ac.ir/article_34954.html}, eprint = {https://scma.maragheh.ac.ir/article_34954_fb1f8292e46d2d8e27e2ad9e34eb5f31.pdf} } @article { author = {Alizadeh, Yahya and Abdollahpour, Mohammad Reza}, title = {Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {37-48}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2019.68582.264}, abstract = {In this paper, we introduce $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frames is a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel multiplier is a p-Schatten class operator.}, keywords = {Controlled continuous $g$-frames,$(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families,Multiplier of continuous $g$-frames}, url = {https://scma.maragheh.ac.ir/article_34963.html}, eprint = {https://scma.maragheh.ac.ir/article_34963_35384b34dcf883a65808ec86a7f3b34c.pdf} } @article { author = {Kalateh Bojdi, Zahra and Askari Hemmat, Ataollah and Tavakoli, Ali}, title = {Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {49-63}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.74791.321}, abstract = {In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.}, keywords = {MRA,Heat equation,wavelet method,Finite difference}, url = {https://scma.maragheh.ac.ir/article_34964.html}, eprint = {https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf} } @article { author = {Vivek, Devaraj and Baghani, Omid and Kanagarajan, Kuppusamy}, title = {Theory of Hybrid Fractional Differential Equations with Complex Order}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {65-76}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.72907.295}, abstract = {We develop the theory of hybrid fractional differential equations with the complex order $\theta\in \mathbb{C}$, $\theta=m+i\alpha$, $0