In this work, a predictor–corrector compact difference scheme for nonlinear fractional differential equation is presented. The MacCormack method provided to deal with terms, the Riemann–Liouville (R-L) integral term treated by means of second-order convolution quadrature formula, and Caputo derivative discretized L1 discrete formula. Through first second derivatives matrix under difference, we ...

In this study, the Lie symmetry analysis is given for time-fractional telegraph equation with Riemann–Liouville derivative. This useable to describe physical processes of models possessing memory. By applying classical and nonclassical α , β derivatives some technical computations, new infinitesimal gen...

The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context fractional-order operators (integrals derivatives). extension performed presented for univariate functions, with aim determining whole set functions satisfying some constraints expressed terms integrals derivatives non-integer order. objective these expressions to so...

Among the many different definitions of fractional derivative, Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider equations with Dzhrbashyan–Nersesyan which generalizes derivatives; it is transformed into such for two sets parameters that are, in a certain sense, symmetric. The issues unique solvability initial value problems some classes linea...

In this paper, we study a nonlinear Riemann-Liouville fractional q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo q-derivative, where terms contain two coupled unknown functions their derivatives. Using fixed point theorem for monotone operators, constructe iteration arbitrary initial value acquire existence uniqueness of extremal solutions. Moreov...

This paper is mainly concerned with feedback control systems governed by fractional impulsive evolution equations involving Riemann–Liouville derivatives in reflexive Banach spaces. We firstly give an existence and uniqueness result of mild solutions for the equations by applying the Banach’s fixed point theorem. Next, by using the Filippove theorem and the Cesari property, a new set of suffici...

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag–Leffler function,...

The article is dedicated towards the study of fractional order nonlinear differential systems with non-instantaneous impulses involving Riemann–Liouville derivatives fixed lower limits and appropriate integral type initial conditions in Banach spaces. First, a mild solution system constructed, subsequently, its existence proven using Banach's point theorem. Then, results approximate controllabi...