Existence Results for Certain Multi-Orders Impulsive Fractional Boundary Value Problem

Bouzaroura, Asma; Mazouzi, Said

doi:10.1007/s00025-014-0403-5

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…Such process is investigated in various fields such as biology, physics, control theory, population dynamics, economics, chemical technology, medicine and so on. For the study for impulsive differential equation, we refer to monograph [10,11], and papers [12][13][14][15][16][17][18][19][20][21][22][23] and references given therein.…”

Section: Introductionmentioning

confidence: 99%

Approximations of Solutions for an Impulsive Fractional Differential Equation with a Deviated Argument

Chaddha

Pandey

2015

Int. J. Appl. Comput. Math

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In the present work, we consider an impulsive fractional differential equation with a deviated argument in an arbitrary separable Hilbert space H . We obtain an associated integral equation and then consider a sequence of approximate integral equations. The existence and uniqueness of solutions to every approximate integral equation is obtained by using analytic semigroup and Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We study the Faedo-Galerkin approximation of the solution and establish some convergence results. Finally, we consider an example to show the effectiveness of obtained theory.

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Section: Introductionmentioning

confidence: 99%

Approximations of Solutions for an Impulsive Fractional Differential Equation with a Deviated Argument

Chaddha

Pandey

2015

Int. J. Appl. Comput. Math

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“…For in this field memory effects are important, hence it is more realistic to use fractional order derivatives, which express the fact that the next state of the system depends not only upon its current state but also upon all of its historical states (see, e.g., [26][27][28]). Moreover, the above type of nonlinear functions arises also in mathematical problems dealing with heat flow in materials with memory and in viscoelastic problems, where the integral term represents the viscosity part; see, for example, [29].…”

Section: Introductionmentioning

confidence: 99%

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

Benedetti

Obukhovskiĭ

Taddei

2015

Journal of Function Spaces

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Functional impulsive differential equation of order α∈(1,2) with nonlocal initial and integral boundary conditions

Gupta

Dabas

2016

Math Methods in App Sciences

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The main work is related to show the existence and uniqueness of solution for the fractional impulsive differential equation of order α∈(1,2) with an integral boundary condition and finite delay. Using the application of the Banach and Sadovaskii fixed‐point theorems, we obtain the main results. An example is presented at the end to verify the results of the paper. Copyright © 2016 John Wiley & Sons, Ltd.

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Existence Results for Certain Multi-Orders Impulsive Fractional Boundary Value Problem

Cited by 5 publications

References 23 publications

Approximations of Solutions for an Impulsive Fractional Differential Equation with a Deviated Argument

Approximations of Solutions for an Impulsive Fractional Differential Equation with a Deviated Argument

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

Functional impulsive differential equation of order α∈(1,2) with nonlocal initial and integral boundary conditions

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