This paper investigates the approximate controllability and optimal controls of fractional dynamical systems order $1< q<2$ in Banach spaces. We research a class governed by integrodifferential equations with nonlocal initial conditions. Using Krasnosel’skii fixed point theorem Schauder theorem, results are obtained under two cases nonlinear term. also present existence pairs corresponding control Bolza cost function. Finally, an application is given to illustrate effectiveness our main results.

In this paper, the fractional Broer–Kaup (BK) system is investigated by studying its novel computational wave solutions. These solutions are constructed applying two recent analytical schemes (modified Khater method and sech–tanh function expansion method). The BK simulates bidirectional propagation of long waves in shallow water. Moreover, it used to study interaction between nonlinear dispersive gravity waves. A new operator convert form a ordinary differential with an integer order. Many...

This research paper studies the semi-analytical, and numerical solutions of on nonlinear long-short wave interaction system which represents an optical field that does not alter through multiplication due to a sensitive balance between linear impacts in elastic medium is defined as can adjust figure consequence deforming strength come back its shape original form when force eliminates. In this medium, produced by vibrations are acoustic power known sound or wave. The Adomian decomposition...

This research paper studies the soliton waves of (N + 1) dimensional time-fractional conformable Sinh-Gordon equation by implementation modified Khater method. surfaces constant negative curvature, such as Gauss-Codazzi for curvature. Using Painlevé property is employed to support method in formulating abundant traveling wave solutions. The performance used technique emphasizes power, effect, and ability applying many nonlinear evolution equations.

We firstly study the existence of PC-mild solutions for impulsive fractional semilinear integrodifferential equations and then present controllability results systems in Banach spaces. The method we adopt is based on fixed point theorem, semigroup theory, generalized Bellman inequality. obtained this paper improve extend some known results. At last, an example presented to demonstrate applications our main

A computational scheme is employed to investigate various types of the solution fractional nonlinear longitudinal strain wave equation. The novelty and advantage proposed method are illustrated by applying this model. new definition used convert formula these equations into integer-order ordinary differential equations. Soliton, rational functions, trigonometric function, hyperbolic many other explicit solutions obtained.

Abstract In this paper, under the assumption that corresponding linear system is approximately controllable, we obtain approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The results are proved by means Hölder inequality, Banach contraction mapping principle, and Schauder fixed point theorem. We also discuss existence optimal controls for controlled systems. Finally, an example given to illustrate applications main results. MSC: 26A33, 49J15, 49K27, 93B05, 93C25.

This paper is concerned with the existence results of nonlocal problems for a class fractional impulsive integrodifferential equations in Banach spaces. We define piecewise continuous control function to obtain on controllability corresponding systems. The are obtained by means fixed point methods. An example illustrate applications our main given.

In this paper, the controllability of a class fractional differential evolution equations with nonlocal conditions is investigated.Sufficient which guarantee are obtained.The method used contraction mapping principle and Krasnoselskii theorem.A distributed parameter control system provided to illustrate applications our results.

Abstract We consider the controllability problem for a class of fractional evolution systems mixed type in an infinite dimensional Banach space. The existence mild solutions and results are discussed by new estimation technique measure noncompactness fixed point theorem with respect to convex-power condensing operator. However, main do not need any restrictive conditions on estimated parameters noncompactness. Since we assume that semigroup is compact other more general, outcomes obtain here...

We establish several oscillation criteria for a class of third-order nonlinear dynamic equations with damping term and nonpositive neutral coefficient by using the Riccati transformation. Two illustrative examples are presented to show significance results obtained.

This manuscript studies the computational solutions of highly dimensional elastic and nonelastic interaction between internal waves through fractional nonlinear (4 + 1)-dimensional Fokas equation. equation is considered as extension model two-dimensional Davey–Stewartson (DS) Kadomtsev–Petviashvili (KP) equations to a four spatial dimensions with time domain. The modified Khater method employed along Atangana–Baleanu (AB) derivative operator construct many novel explicit wave solutions....

This paper is concerned with adaptive control for anti-synchronization of a class uncertain fractional-order chaotic complex systems described by unified mathematical expression.By utilizing the recently established result Caputo fractional derivative quadratic function and employing technique, we design controllers some parameter update laws to anti-synchronize two unknown parameters.The proposed method has generality, simplicity, feasibility.Moreover, between Lorenz system L ü implemented...

The Gronwall inequalities are of significance in mathematics and engineering. This paper generalizes the Gronwall-like from different perspectives. Using proposed inequalities, difficulties to discuss controllability integrodifferential systems mixed type can be solved. Meanwhile, two examples as their applications also given show effectiveness our main results.

This research paper investigates the stable computational, semi-analytical, and numerical solutions of nonlinear complex fractional generalized–Zakharov system. system describes interactions between low-frequency, acoustic waves high-frequency, electromagnetic waves. The modified Khater method is applied to find analytical then stability property these discussed by using Hamiltonian properties. Moreover, computational are used as initial condition in semi-analytical schemes. Adomian...

In the upcoming fifth-generation (5G) ecosystem, delivery of a variety personalized services is envisioned. With development software-defined networks and network function virtualization technologies, display increasingly flexible features, such as programmability. Network slicing state-of-the-art technology that provides tailored to specific demands users, smart grids e-health applications. this article, we introduce concept its application discuss related work. addition, propose an...

This paper investigates the existence and uniqueness ofmild solutions for fractional impulsive integro-differentialevolution equations with nonlocal 条件 of order$1<\\beta\\leq2$. Under two cases where 解 operator iscompact noncompact respectively, results mild areestablished by (generalized) Darbo fixed point 定理 andSchauder 定理. Meanwhile, mildsolutions is also given Banach contractionmapping principle. These are obtained semigroup定理, theorems, measures noncompactness andfixed At last, an 例...

It is well-known that controllability closely linked to pole assignment, structural decomposition, quadratic optimal control and observer design, then the study of plays an important role in theory engineering. In this paper, using mönch fixed point theorem estimate step by step, nonlocal boundary conditions for impulsive differential systems mixed type Banach spaces investigated. Under weaker conditions, some sufficient are obtained. The results improve extend known results. An example...

In this paper, controllability of nonlinear fractional composite dynamical systems order  in finite-dimensional spaces is investigated. Solution represents linear and are defined. The method used paper Mittag-Leffler matrix function iterative technique. An example provided to illustrate effectiveness the main result.