in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1 < · · · < qr < 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with...

This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. examines the construction of solutions equations are associated varying delay proportional to independent variable using a hybrid Sumudu transform method. considers Caputo derivatives orders their applications in Nuclear Physics. The application indicates have...

Abstract The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive integral boundary conditions. concerned involves proportional type delay term. By using Schaefer’s fixed point theorem Banach’s contraction principle, the required conditions are developed. Also, differ...

Abstract In this paper, we study an initial value problem for a class of impulsive implicit-type fractional differential equations (FDEs) with proportional delay terms. Schaefer’s fixed point theorem and Banach’s contraction principle are the key tools in obtaining required results. We apply our results to numerical demonstration purpose.