<abstract xmlns="http://www.w3.org/1999/xhtml">In surveys covering human populations it is observed that information in most cases are not obtained at the first attempt even after some callbacks. Such problems come under the category of non-response. Surveys suffer with non-response in various ways. It depends on the nature of required information, either surveys is concerned with general or sensitive issues of a society. <xref ref-type="bibr" rid="j_jamsi-2016-0006_ref_003_w2aab2b8b4b1b7b1ab1ab3Aa">Hansen and Hurwitz (1946)</xref> have considered the problem of non-response while estimating the population mean by taking a subsample from the non-respondent group with the help of extra efforts and an estimator was suggested by combining the information available from the response and nonresponse groups. We also mention that in survey sampling auxiliary information is commonly used to improve the performance of an estimator of a quantity of interest. For estimating the population mean using auxiliary information in presence of non-response has been discussed by various authors. In this paper, we have developed estimators for estimating the population mean of the variable under interest when there is non-response error in the study as well as in the auxiliary variable. We have studied properties of the suggested estimators under large sample approximation. Comparison of the suggested estimators with usual unbiased estimator reported by <xref ref-type="bibr" rid="j_jamsi-2016-0006_ref_003_w2aab2b8b4b1b7b1ab1ab3Aa">Hansen and Hurwitz (1946)</xref> and the ratio estimator due to <xref ref-type="bibr" rid="j_jamsi-2016-0006_ref_011_w2aab2b8b4b1b7b1ab1ac11Aa">Rao (1986)</xref> have been made. The results obtained are illustrated with aid of an empirical study.</abstract>

School of Studies in Statistics, Vikram University, Ujjain-456010, M.P.,

Finite Population Mean Estimation through a Two-Parameter Ratio Estimator Using Auxiliary Information in Presence of Non-Response

<abstract xmlns="http://www.w3.org/1999/xhtml">Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.</abstract>

Department of Mathematics, Faculty of Science, Selçuk University, Konya,

Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay,

New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">We establish generalized pre-Grüss inequality for local fractional integrals. Then, we obtain some inequalities involving generalized expectation, <italic>p−</italic>moment, variance and cumulative distribution function of random variable whose probability density function is bounded. Finally, some applications for generalized Ostrowski-Grüss inequality in numerical integration are given.</abstract>

Department of Mathematics, Faculty of Science, Bartın University, Bartın-

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce-

Department of Statistics, Faculty of Science, Bartın University, Bartın-

Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on fractional fuzzy initial value problem (FFIVP) with triangular condition. Here, Legendre polynomials are used to modify the structure of neural networks with a Taylor series approximation of the tangent hyperbolic as activation function while the network adaptive coefficients are trained in the procedure of simulated annealing to optimize the residual error. The computational results are depicted in terms of numerical values to compare them with previous results.</abstract>

Department of Mathematics, University of Karachi, Karachi 75270,

Department of Mathematics, of Karachi, Karachi 75270,

Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock,

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study we apply the Adomian decomposition method (ADM) to approximate the solution of fractional optimal control problems (FOCPs) where the dynamic of system is a linear control system with constant coefficient and the cost functional is defined in a quadratic form. First we stated the necessary optimality conditions in a form of fractional two point boundary value problem (TPBVP), then the ADM is used to solve the resulting fractional differential equations (FDEs). Some examples are provided to demonstrate the validity and applicability of the proposed method.</abstract>

Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan,

National Iranian Oil Products Distribution Company (NIOPDC), Zahedan Region, Zahedan,

National Iranian Gas Company (NIGC), Zahedan Region, Zahedan,

Approximated Solutions of Linear Quadratic Fractional Optimal Control Problems

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