Explicit solutions of initial value problems for systems of linear Riemann–Liouville fractional differential equations with constant delay

Abstract

A system of linear Riemann-Liouville fractional differential equations with constant delay is studied. The initial condition is set up similar to the case of the ordinary derivative. Explicit formulas for the solutions are obtained for various initial functions.

Time fractional exact controllability

“…The above problem is well-posed by means of a spectral representation and the Mittag-Leffler functions, see e.g. [5,2,4,7,3].…”

Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

“…The fractional calculus is an important branch of mathematics and its wide applications to many fields, such engineering, economics, physics, chemistry, finance, control of dynamical systems, and so on-see [1][2][3][4][5][6][7], and the references cited therein. One of the proposed generalizations of the fractional calculus operators is the ψ-fractional operatorsee [8][9][10] and references therein for its wide applications.…”

On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

“…They also use another approaches and methods for their special aims such as approximate methods and topological methods. One can easily find different modern works on various categories of the fractional differential equations and inclusions, [31][32][33][34][35][36] boundary value problems, [37][38][39][40][41][42] and modeling of different natural phenomena. [43][44][45][46][47][48][49][50][51] In 2016, Ahmad et al studied the existence results for the sequential fractional integro-differential equation with sum boundary value conditions:…”

“…They also use another approaches and methods for their special aims such as approximate methods and topological methods. One can easily find different modern works on various categories of the fractional differential equations and inclusions, 31‐36 boundary value problems, 37‐42 and modeling of different natural phenomena 43‐51 …”