In This paper generalized spline method and Caputo differential operator is applied to solve linear fractional integro-differential equations of the second kind. Comparison of the applied method with exact solutions reveals that the method is tremendously effective.

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

    This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

     In this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it  gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives  better information over whole time interv

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

In this paper, we construct a new mathematical system as Multiplicative Cyclic Group (MCG), called a New Digital Algebraic Generator (NDAG) Unit, which would generate digital sequences with good statistical properties. This new Unit can be considered as a new basic unit of stream ciphers.

A (NDAG) system can be constructed from collection of (NDAG) units using a Boolean function as a combining function of the system. This system could be used in cryptography as like as Linear Feedback Shift Register (LFSR) unit. This unit is basic component of  a stream cipher system.

 In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability  of a one component strengths X under stress Y. Second, reliability  of one component strength under three stresses. Where X and Y are independent generalized exponential-Poison random variables with parameters (α,λ,θ) and (β,λ,θ) . The analysis is concerned with and based on doubly type II censored samples using gamma prior under four different loss functions, namely   quadratic loss function, weighted loss functions,  linear and non-linear exponential loss function. The estimators are compared by mean squared error criteria due to a simulation study. We also find that the mean square error is

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.