Existence of mild solutions for conformable fractional differential equations with nonlocal conditions

Bouaouid, Mohamed; Hilal, Khalid; Melliani, Saïd

doi:10.1216/rmj.2020.50.871

Cited by 13 publications

(9 citation statements)

References 21 publications

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“…Remark 1 ([26]). If D a β y(t 0 ) exists and is finite, we say that y is For more details about conformable derivatives, we can refer to [26,27] and the references therein. Then, we will review the definition of generalized clarke for a locally Lipschitz functional F : X → R on a Banach space X.…”

Section: Preliminariesmentioning

confidence: 99%

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Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities

Hao

Wang

Han

2022

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In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued pseudomonotone operators and the property of the conformable derivative. Notice that we imply some new fractional viscoelastic constitutive laws.

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Section: Preliminariesmentioning

confidence: 99%

“…To overcome the above difficulties, conformable derivatives as a new fractional derivative are proposed in [26]. Recently, conformable derivatives have attracted attention in mathematics and applications, see [27][28][29][30][31][32]. It can describe Newtonian mechanics [29], the logical model [30] and cobweb model [31].…”

Section: Introductionmentioning

confidence: 99%

Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities

Hao

Wang

Han

2022

Axioms

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“…This novel fractional derivative is very simple and verifies all the properties of the classical deriva-tive. Actually, the conformable fractional derivative becomes the subject of many research contributions [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

“…For example in [20][21][22], the authors have proved the existence of mild solution for the following nonlocal conformable fractional Cauchy problem:…”

Section: Introductionmentioning

confidence: 99%

Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations

Hannabou

Bouaouid

Hilal

2022

Advances in Mathematical Physics

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In many research works Bouaouid et al. have proved the existence of mild solutions of an abstract class of nonlocal conformable fractional Cauchy problem of the form: d α x t / d t α = A x t + f t , x t , x 0 = x 0 + g x , t ∈ 0 , τ . The present paper is a continuation of these works in order to study the controllability of mild solution of the above Cauchy problem. Precisely, we shall be concerned with the controllability of mild solution of the following Cauchy problem d α x t / d t α = A x t + f t , x t + B u t , x 0 = x 0 + g x , t ∈ 0 , τ , where d α . / d t α is the vectorial conformable fractional derivative of order α ∈ 0 , 1 in a Banach space X and A is the infinitesimal generator of a semigroup T t t ≥ 0 on X . The element x 0 is a fixed vector in X and f , g are given functions. The control function u is an element of L 2 0 , τ , U with U is a Banach space and B is a bounded linear operator from U into X .

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“…In recent decades, fractional differential equations have been used to describe several natural phenomena in applied sciences such as fluid flow, chemistry, physics, biology, and other areas [1][2][3][4][5], for modeling different phenomena which may depend on the previous time as well as the current time. Besides, fractional differential equations can be considered more efficient to investigate the process of scientific phenomena with complex irregular conditions, see, for example, [6][7][8][9][10][11]. erefore, a large number of powerful methods have been developed to look for exact and numerical solutions such us the variational iteration method [12], transformation method [13], finite-difference method [14], Exp-function method [15], homotopy analysis method [16], Adomian decomposition method [17], the first integral method [18], and sine-cosine method [19].…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation

Maarouf

Maadan

Hilal

2021

International Journal of Differential Equations

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This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdèlyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.

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Existence of mild solutions for conformable fractional differential equations with nonlocal conditions

Cited by 13 publications

References 21 publications

Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities

Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities

Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations

Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation

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