Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.95-105
I. I. Aina, O. J. Peter, A. Ayoade, F. Oguntolu, M. Oluwayemi
Cuckoo Search (CS) algorithm is a meta-heuristic technique that displays several merits. For example, it is easier to apply and less tuning parameters also, it is suitable for solving optimization problems. However, easily fall into local optimum has been established and has a slow convergence rate as a result of the cuckoo search parameters being kept constant. Therefore to handle this issue, an Enhanced Cuckoo Intelligence Search (ECIS) algorithm was developed which is an upgraded CS algorithm. The efficiency of ECIS was tested by some benchmark constrained optimization test functions and it was shown that ECIS gives a better optimal value than CS.
{"title":"Enhanced Cuckoo Intelligence Search Algorithm","authors":"I. I. Aina, O. J. Peter, A. Ayoade, F. Oguntolu, M. Oluwayemi","doi":"10.37622/ijde/16.1.2021.95-105","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.95-105","url":null,"abstract":"Cuckoo Search (CS) algorithm is a meta-heuristic technique that displays several merits. For example, it is easier to apply and less tuning parameters also, it is suitable for solving optimization problems. However, easily fall into local optimum has been established and has a slow convergence rate as a result of the cuckoo search parameters being kept constant. Therefore to handle this issue, an Enhanced Cuckoo Intelligence Search (ECIS) algorithm was developed which is an upgraded CS algorithm. The efficiency of ECIS was tested by some benchmark constrained optimization test functions and it was shown that ECIS gives a better optimal value than CS.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85425192","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.107-122
P. Selvakumar, P. Gopalakrishnan, A. Murugesan
We obtained oscillation criteria for the second-order half-linear neutral advanced difference equations of the kind ∆(α(ζ)(∆w(ζ))) + η(ζ)y(ζ + κ) = 0; ζ ≥ ζ0, where w(ζ) = y(ζ) + p(ζ)y(ζ + ξ). We provide a new oscillation condition, which significantly improves the existing ones, by providing a new axiom bound for a non-oscillatory solution. The derived oscillation constant is unimprovable in a certain nonneutral case. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.
{"title":"New Oscillation Criteria for Half-Linear Second-Order Neutral Advanced Difference Equations","authors":"P. Selvakumar, P. Gopalakrishnan, A. Murugesan","doi":"10.37622/ijde/16.1.2021.107-122","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.107-122","url":null,"abstract":"We obtained oscillation criteria for the second-order half-linear neutral advanced difference equations of the kind ∆(α(ζ)(∆w(ζ))) + η(ζ)y(ζ + κ) = 0; ζ ≥ ζ0, where w(ζ) = y(ζ) + p(ζ)y(ζ + ξ). We provide a new oscillation condition, which significantly improves the existing ones, by providing a new axiom bound for a non-oscillatory solution. The derived oscillation constant is unimprovable in a certain nonneutral case. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84069657","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.59-79
K. Yadav
Wavelet analysis is well developed mathematical tool which can be also applied in numerical analysis. Here application of the Haar wavelet techniques has been discussed for finding numerical solution of fifth-order boundary value problems. Accuracy of the considered technique is demonstrated by means of three numerical examples, taken from well existing research article. Mathematics Subject Classification (2000). 65L10, 65T60.
{"title":"A Comparative Study of Approximate Solution of Fifth-order Boundary-value Problems by Applying HaarWavelets Technique and Galerkin Method with Quartic B-splines","authors":"K. Yadav","doi":"10.37622/ijde/16.1.2021.59-79","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.59-79","url":null,"abstract":"Wavelet analysis is well developed mathematical tool which can be also applied in numerical analysis. Here application of the Haar wavelet techniques has been discussed for finding numerical solution of fifth-order boundary value problems. Accuracy of the considered technique is demonstrated by means of three numerical examples, taken from well existing research article. Mathematics Subject Classification (2000). 65L10, 65T60.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"115 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80833640","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.19-34
A. El-Sayed, W. El-Sayed, Somyya S. Amrajaa
Here, we study the existence of solutions of a nonlocal two-point with parameters boundary value problem of a first order nonlinear differential inclusion. The maximal and minimal solutions will be studied. The continuous dependence of the unique solution on the parameters of the nonlocal condition will be proved. The anti-periodic boundary value problem will be considered as an application
{"title":"A Nonlocal (Two-point with Parameters) Boundary Value Problem of Differential Inclusion","authors":"A. El-Sayed, W. El-Sayed, Somyya S. Amrajaa","doi":"10.37622/ijde/16.1.2021.19-34","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.19-34","url":null,"abstract":"Here, we study the existence of solutions of a nonlocal two-point with parameters boundary value problem of a first order nonlinear differential inclusion. The maximal and minimal solutions will be studied. The continuous dependence of the unique solution on the parameters of the nonlocal condition will be proved. The anti-periodic boundary value problem will be considered as an application","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84901203","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.11-17
Hwajoon Kim
{"title":"Laplace Transform of Discriminant for Functions of Second Variable and its Generalized Form","authors":"Hwajoon Kim","doi":"10.37622/ijde/16.1.2021.11-17","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.11-17","url":null,"abstract":"","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76545256","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.81-93
O. Fadipe-Joseph, M. Oluwayemi, E. Titiloye
The authors obtained some geometric results on certain new classes of analytic functions involving sigmoid function defined by Fadipe-Joseph et. al. 2016 as Tγ(λ, β, α, μ). Extreme point property, radius of starlikeness and convexity, convolution property and Fekete-Szego inequality for the class were proved.
{"title":"Subclasses of Univalent Functions Involving Modified Sigmoid Function","authors":"O. Fadipe-Joseph, M. Oluwayemi, E. Titiloye","doi":"10.37622/ijde/16.1.2021.81-93","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.81-93","url":null,"abstract":"The authors obtained some geometric results on certain new classes of analytic functions involving sigmoid function defined by Fadipe-Joseph et. al. 2016 as Tγ(λ, β, α, μ). Extreme point property, radius of starlikeness and convexity, convolution property and Fekete-Szego inequality for the class were proved.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"2015 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86968848","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.47-57
Yogita m. Ahire, N. M. Mohammed, Ahmed A. Hamoud
In this study, the semigroup theory and the Schauder fixed point theorem are applied to prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra-Fredholm integro-differential equation of Sobolev type with nonlocal condition.
{"title":"Results on the Existence of Solutions of Sobolev-Type Volterra-Fredholm Integro-Differential Equations","authors":"Yogita m. Ahire, N. M. Mohammed, Ahmed A. Hamoud","doi":"10.37622/ijde/16.1.2021.47-57","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.47-57","url":null,"abstract":"In this study, the semigroup theory and the Schauder fixed point theorem are applied to prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra-Fredholm integro-differential equation of Sobolev type with nonlocal condition.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76779833","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.123-135
C. Rajan, A. Murugesan, P. Gopalakrishnan
We derive oscillatory conditions for the second-order delay difference equation ∆ ( φ(ζ)(∆v(ζ)) ) + μ(ζ)x(η(ζ)) = 0; ζ ≥ ζ0, where v(ζ) = x(ζ) + ∑m i=1 pi(ζ)x i(κi(ζ)). We investigate oscillatory behavior for the cases when ξ > ν and ξ < ν. Many results presented in the literature are supplemented and improved by this new theorem. Finally, we give some examples to show our major findings. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.
{"title":"New Oscillation Conditions for Second-Order Delay Difference Equations with Several Sub-Linear Neutral Terms","authors":"C. Rajan, A. Murugesan, P. Gopalakrishnan","doi":"10.37622/ijde/16.1.2021.123-135","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.123-135","url":null,"abstract":"We derive oscillatory conditions for the second-order delay difference equation ∆ ( φ(ζ)(∆v(ζ)) ) + μ(ζ)x(η(ζ)) = 0; ζ ≥ ζ0, where v(ζ) = x(ζ) + ∑m i=1 pi(ζ)x i(κi(ζ)). We investigate oscillatory behavior for the cases when ξ > ν and ξ < ν. Many results presented in the literature are supplemented and improved by this new theorem. Finally, we give some examples to show our major findings. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"53 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75445983","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}
Pub Date : 2021-06-30DOI: 10.37622/ijde/16.1.2021.169-178
Mohammed Elmoudier, M. Gobar
This paper introduces a method to evaluate the efficiency of a random sample from some sampling distributions. The Shannon entropy and A-entropy are considered to calculate the efficiency of such samples. The obtained results are discussed. An example is given to illustrate the computations of efficiency of random sample from the geometric, binomial and Poisson distributions.
{"title":"Efficiency Sample From Some Sampling Distributions","authors":"Mohammed Elmoudier, M. Gobar","doi":"10.37622/ijde/16.1.2021.169-178","DOIUrl":"https://doi.org/10.37622/ijde/16.1.2021.169-178","url":null,"abstract":"This paper introduces a method to evaluate the efficiency of a random sample from some sampling distributions. The Shannon entropy and A-entropy are considered to calculate the efficiency of such samples. The obtained results are discussed. An example is given to illustrate the computations of efficiency of random sample from the geometric, binomial and Poisson distributions.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78977110","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}
Pub Date : 2020-12-30DOI: 10.37622/IJDE/15.2.2020.191-195
Haegyeong Han, Hwajoon Kim
We consider the solution of exponential growth and exponential decay by using Laplace transform. In that an arbitrary constant can be specifically expressed as the initial value, the proposed method has a meaning.
{"title":"The Solution of Exponential Growth and Exponential Decay by Using Laplace Transform","authors":"Haegyeong Han, Hwajoon Kim","doi":"10.37622/IJDE/15.2.2020.191-195","DOIUrl":"https://doi.org/10.37622/IJDE/15.2.2020.191-195","url":null,"abstract":"We consider the solution of exponential growth and exponential decay by using Laplace transform. In that an arbitrary constant can be specifically expressed as the initial value, the proposed method has a meaning.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77503047","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}
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