{"title":"One Solution of Multi-term Fractional Differential Equations by Adomian Decomposition Method: Scientific Explanation","authors":"Abdollah Sadeghinia, P. Kumar","doi":"10.9734/BPI/CTMCS/V6/11542D","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/11542D","url":null,"abstract":"The Adomian decomposition method (ADM) is a well-known for analytical approximate solutions of linear or nonlinear ordinary differential equations (ODEs), Fractional Differential Equations (FDEs) , integral equations ,integral differential equations, etc. They arevery useful for application oriented problems .Numerical method is to obtain approximate solutions of fractional differential equations.Forexamples Legendre Pseudo-Spectral Method,vibrational iteration method, etc. H.Jafari andV.Gejji [5,10] have solved a system of nonlinear fractional differential equations and a multi order fractional differential equation using Adomian decomposition for nonlinear is functions of .In 2006,S.Momania and Zaid Odibatb[7] used the vibrational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order . O.A. Taiwo and O.S. Odetunde [8]applied approximation of multi-order fractional differential equations by an iterative decomposition method. M. M. Khader, talaat S. El danaf and A. S. Hendy [9],used efficient spectral collocation method for solving multi-term fractional differential equations based on the generalized laguerre polynomials .VedatSuatErturkShaher Momani B, Zaid Odibat [6] presented application of generalized differential transform method to multi-order fractional differential equations. In this paper we consider the Multi-term Fractional Differential Equations as form:","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130670684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Study on the Generalized Fuzzy Mean Codeword Lengths","authors":"D. Hooda, D. Jain","doi":"10.9734/BPI/CTMCS/V6/3167F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3167F","url":null,"abstract":"Information Theory has ideas which are widely applicable to the situations remote from its original inspiration. Although, the applicability of ideas is not always exact; yet these are very useful. One of the best applications of information measure is noiseless coding theorem which provides the bounds for suitable encoding of entropies and fuzzy information measures.\u0000In present chapter, mean code word and fuzzy mean codeword lengths are defined, and some generalizations of mean codeword length are also described. A generalized fuzzy mean codeword length of degree (beta) is defined and its bounds in the term of a generalized fuzzy information measure are studied. Further, the fuzzy mean codeword length of type ((alpha), (beta)) is introduced and its bounds are studied. Monotonic behavior of these fuzzy mean codeword lengths is illustrated graphically by taking some empirical data.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131145308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}