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Properties of Green’s function and the existence of different types of solutions for nonlinear fractional BVP with a parameter in integral boundary conditions

Wenxia Wang

Boundary Value Problems > 2019 > 2019 > 1 > 1-20

This paper is concerned with the impact of the parameter on the existence of different types of solutions for a class of nonlinear fractional integral boundary value problems with a parameter that causes the sign of Green’s function associated with the BVP to change. By using the Guo–Krasnoselskii fixed point theorem, the Leray–Schauder nonlinear alternative, and the analytic technique, we give the...

article

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Saïd Abbas, Mouffak Benchohra, Johnny Henderson, Boualem Attou Slimani

Journal of Applied Mathematics and Computing > 2016 > 52 > 1-2 > 73-85

In this paper, we prove an existence result and we initiate the question of attractivity of solutions for initial value problems (IVP for short), for fractional order neutral differential equations with finite delay. The proof of the main result is based on Krasnosel’skii’s fixed point theorem.

article

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Saïd Abbas, Mouffak Benchohra, Mohamed Abdalla Darwish

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2016 > 36 > 2 > 155-179

In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions

article

Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses

Saïd Abbas, Mouffak Benchohra

Applied Mathematics and Computation > 2015 > 257 > Complete > 190-198

In this paper, we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations for a class of partial functional differential equations with not instantaneous impulses in Banach spaces. An example is also provided to illustrate our results.

article

Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter

Chengbo Zhai, Li Xu

Communications in Nonlinear Science and Numerical Simulation > 2014 > 19 > 8 > 2820-2827

In this paper, by using fixed point theorems of concave operators in partial ordering Banach spaces, we establish the existence and uniqueness of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations for any given parameter. Moreover, we present some pleasant properties of positive solutions to the boundary value problem dependent on the parameter...

article

Ulam–Hyers Stability for the Darboux Problem for Partial Fractional Differential and Integro-differential Equations via Picard Operators

Saïd Abbas, Mouffak Benchohra

Results in Mathematics > 2014 > 65 > 1-2 > 67-79

In the present paper we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations due to Rus, for the Darboux problem of partial differential and integro-differential equations involving the Caputo fractional derivative. Our results are obtained by using weakly Picard operators theory.

article

Matrix method for numerical solution of space-time fractional diffusion-wave equations with three space variables

Mridula Garg, Pratibha Manohar

Afrika Matematika > 2014 > 25 > 1 > 161-181

In the present paper we solve space-time fractional diffusion-wave equations with three space variables, using matrix method. Here, in particular we give solutions to classical, time-fractional, space-fractional and space-time fractional diffusion equations and classical, time-fractional, space-fractional and space-time fractional wave equations with different combinations of time and space fractional...

article

On a nonlocal problem for fractional differential equations via resolvent operators

Lizhen Chen, Zhenbin Fan, Gang Li

Advances in Difference Equations > 2014 > 2014 > 1 > 1-12

Using the techniques of approximate solutions, the analytic resolvent method, and the uniform continuity of the resolvent, we discuss the existence of mild solutions for nonlocal fractional differential equations governed by a linear closed operator which generates a resolvent. An example is also given to illustrate the application of our theory. MSC: 34K37, 47A10.

article

Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order

Saïd Abbas, Mouffak Benchohra

Nonlinear Analysis: Hybrid Systems > 2010 > 4 > 3 > 406-413

In this paper we investigate the existence of solutions for a class of initial value problems for impulsive partial hyperbolic differential equations involving the Caputo fractional derivative by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

article

Darboux problem for perturbed partial differential equations of fractional order with finite delay

Saïd Abbas, Mouffak Benchohra

Nonlinear Analysis: Hybrid Systems > 2009 > 3 > 4 > 597-604

In this paper we investigate the existence of solutions for functional partial perturbed hyperbolic differential equations with fractional order. These results are based upon a fixed point theorem for the sum of contraction and compact operators.

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Keywords

CAPUTO FRACTIONAL ORDER DERIVATIVE (10)
FIXED POINT (4)
DARBOUX PROBLEM (3)
LEFT-SIDED MIXED RIEMANN–LIOUVILLE INTEGRAL (3)
FIXED POINT EQUATION (2)
FRACTIONAL DIFFERENTIAL EQUATION (2)
FRACTIONAL ORDER (2)
LEFT-SIDED MIXED RIEMANN-LIOUVILLE INTEGRAL (2)
LOWER SOLUTION (2)
PARAMETER (2)
UPPER SOLUTION (2)
ANALYTIC RESOLVENT (1)
ATTRACTIVITY (1)
BANACH ALGEBRAS (1)
CONE (1)
CONTRACTION (1)
DELAY (1)
DISCRETIZATION (1)
EXTREMAL SOLUTION (1)
FIXED POINT THEOREMS OF CONCAVE OPERATOR (1)
FOUR-POINT BOUNDARY VALUE PROBLEM (1)
FRACTIONAL DIFFERENTIAL INCLUSION (1)
FRACTIONAL DIFFUSION-WAVE EQUATION (1)
FUNCTIONAL DIFFERENTIAL EQUATIONS (1)
FUNCTIONAL NEUTRAL DIFFERENTIAL EQUATIONS (1)
IMPULSE (1)
IMPULSIVE HYPERBOLIC DIFFERENTIAL EQUATION (1)
INTEGRAL BOUNDARY VALUE PROBLEM (1)
INTEGRO-DIFFERENTIAL EQUATION (1)
KRONECKER MATRIX PRODUCT (1)
MATRIX APPROACH (1)
MILD SOLUTION (1)
NONLOCAL CONDITIONS (1)
NOT INSTANTANEOUS IMPULSES (1)
POSITIVE SOLUTION (1)
RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE (1)
SIGN-CHANGING SOLUTION (1)
SOLUTION (1)
SYMMETRIC-RIESZ FRACTIONAL DERIVATIVE (1)
ULAM–HYERS STABILITY (1)
ULAM–HYERS–RASSIAS STABILITY (1)
WEEKLY PICARD OPERATOR (1)
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Springer (5)
Elsevier (4)
DML (1)

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