In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.
{"title":"Numerical solution of the conformable fractional diffusion equation","authors":"H. Yaslan","doi":"10.18514/mmn.2022.3669","DOIUrl":"https://doi.org/10.18514/mmn.2022.3669","url":null,"abstract":"In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68201844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove the existence of infinitely many solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponents and obtain new conclusion under different conditions. The methods used here are based on variational methods and LjusternikSchnirelmann theory.
{"title":"Multiple solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponent","authors":"Tiantian Zheng, Chunyan Zhang, Jihui Zhang","doi":"10.18514/mmn.2022.3926","DOIUrl":"https://doi.org/10.18514/mmn.2022.3926","url":null,"abstract":"In this paper, we prove the existence of infinitely many solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponents and obtain new conclusion under different conditions. The methods used here are based on variational methods and LjusternikSchnirelmann theory.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68203261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We classify all possible local linear procedures on triangular meshes resulting in polynomial C1-spline functions with affinely uniform shape conditions for the basic functions at the edges, and fitting the 9 value and gradient data at the vertices of the mesh triangles. There is a unique procedure among them with shape functions and basic polynomials of degree 5 and all other admissible procedures are its perturbations with higher degree.
{"title":"Locally generated Hermitian C1-splines on triangular meshes","authors":"L. Stachó","doi":"10.18514/mmn.2022.3399","DOIUrl":"https://doi.org/10.18514/mmn.2022.3399","url":null,"abstract":"We classify all possible local linear procedures on triangular meshes resulting in polynomial C1-spline functions with affinely uniform shape conditions for the basic functions at the edges, and fitting the 9 value and gradient data at the vertices of the mesh triangles. There is a unique procedure among them with shape functions and basic polynomials of degree 5 and all other admissible procedures are its perturbations with higher degree.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68200726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local existence and blow up for p-Laplacian equation with logarithmic nonlinearity","authors":"Nazlı Irkıl, E. Pişkin","doi":"10.18514/mmn.2022.3490","DOIUrl":"https://doi.org/10.18514/mmn.2022.3490","url":null,"abstract":"","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68200763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Common terms of Tribonacci and Perrin sequences","authors":"Abdullah Açikel, N. Irmak","doi":"10.18514/mmn.2022.3611","DOIUrl":"https://doi.org/10.18514/mmn.2022.3611","url":null,"abstract":"","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68200946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results.
{"title":"Existence and nonexistence of positive solutions for the second-order m-point eigenvalue impulsive boundary value problem","authors":"D. Oz, I. Karaca","doi":"10.18514/mmn.2022.3767","DOIUrl":"https://doi.org/10.18514/mmn.2022.3767","url":null,"abstract":"This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68202713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On e-Convexity","authors":"M. H. Alizadeh, J. Makó","doi":"10.18514/mmn.2022.2467","DOIUrl":"https://doi.org/10.18514/mmn.2022.2467","url":null,"abstract":"","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68199150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, solution of complex partial derivative equations with variable coefficients from the first and second order have been investigated. For this solution, an iteration relation was obtained using the reduced differential transform method. This method also was been applied for ordinary complex differential equations which examined in the literature. The solution which has been obtained has been seen compatible with the literature.
{"title":"Solution of complex differential equations with variable coefficients by using reduced differential transform","authors":"M. Düz","doi":"10.18514/mmn.2022.3442","DOIUrl":"https://doi.org/10.18514/mmn.2022.3442","url":null,"abstract":"In this article, solution of complex partial derivative equations with variable coefficients from the first and second order have been investigated. For this solution, an iteration relation was obtained using the reduced differential transform method. This method also was been applied for ordinary complex differential equations which examined in the literature. The solution which has been obtained has been seen compatible with the literature.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68200623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deferred Cesaro statistical convergence of martingale sequence and Korovkin-type approximation theorems","authors":"H. Srivastava, B. Jena, S. K. Paikray","doi":"10.18514/mmn.2022.3624","DOIUrl":"https://doi.org/10.18514/mmn.2022.3624","url":null,"abstract":"","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68200895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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