Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution

We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. Two examples related to fractional-order Hopfield neural networks with constant external inputs and a marine protected area model are introduced to illustrate the applicability of stability results.

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LYAPUNOV-TYPE INEQUALITIES FOR LOCAL FRACTIONAL DIFFERENTIAL SYSTEMS

Fractals ◽

10.1142/s0218348x20501315 ◽

2020 ◽

Vol 28 (07) ◽

pp. 2050131

Author(s):

YONGFANG QI ◽

LIANGSONG LI ◽

XUHUAN WANG

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Analytical Method ◽

Systematic Design ◽

Differential Systems ◽

Design Algorithm ◽

Fractional Differential Systems ◽

Lyapunov Inequalities ◽

Fractional Differential

This paper deals with the problem of Lyapunov inequalities for local fractional differential equations with boundary conditions. By using analytical method, a novel Lyapunov-type inequalities for the local fractional differential equations is provided. A systematic design algorithm is developed for the construction of Lyapunov inequalities.

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Analytic Approach for Solving System of Fractional Differential Equations

Al-Mustansiriyah Journal of Science ◽

10.23851/mjs.v32i1.929 ◽

2021 ◽

Vol 32 (1) ◽

pp. 14

Author(s):

Nabaa N Hasan ◽

Zainab John

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Fractional Differential Equations ◽

Caputo Fractional Derivative ◽

Initial Conditions ◽

Analytic Approach ◽

Differential Systems ◽

Fractional Differential Systems ◽

Fractional Differential

In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear fractional differential systems. This formula is applied with Mittage-Leffler function for certain homogenous and nonhomogenous fractional differential systems with nonzero initial conditions. Stability is discussed by means of the system's distinctive equation.

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ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-ORDERS

Fractals ◽

10.1142/s0218348x07003472 ◽

2007 ◽

Vol 15 (02) ◽

pp. 173-182 ◽

Cited By ~ 26

Author(s):

WEIHUA DENG ◽

CHANGPIN LI ◽

QIAN GUO

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Initial Conditions ◽

Rational Numbers ◽

The Other ◽

Differential Systems ◽

Fractional Differential Systems ◽

Stability Theorems ◽

Fractional Differential ◽

Fractional Orders

In this paper, we study two kinds of fractional differential systems with multi-orders. One is a system of fractional differential equations with multi-order, [Formula: see text], [Formula: see text]; the other is a multi-order fractional differential equation, [Formula: see text]. By the derived technique, such two kinds of fractional differential equations can be changed into equations with the same fractional orders providing that the multi-orders are rational numbers, so the known theorems of existence, uniqueness and dependence upon initial conditions are easily applied. And asymptotic stability theorems for their associate linear systems, [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], [Formula: see text], are also derived.

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