scholarly journals On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zareen A. Khan ◽  
Rozi Gul ◽  
Kamal Shah
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Order Derivative ◽  
Liouville Type ◽  
Fractional Order Derivative ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Boundary Value Problem ◽  
The Subject

Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence and puniness of a solution to the proposed problem. For our required results, we utilize the classical fixed point theorems from Banach and Scheafer. It is to be noted that the impulsive boundary value problem under the fractional order derivative of the Riemann-Liouville type has been very rarely considered in literature. Finally, to demonstrate the obtained results, we provide some pertinent examples.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

2015 ◽  
Vol 08 (04) ◽  
pp. 1550057 ◽  
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

scholarly journals Impulsive Boundary Value Problems for Planar Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zeynep Kayar ◽  
Ağacık Zafer
Keyword(s):  
Boundary Value Problem ◽  
Hamiltonian Systems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Type Inequality ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of Solutions ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Boundary Value Problem ◽  
Lyapunov Type Inequality

We give an existence and uniqueness theorem for solutions of inhomogeneous impulsive boundary value problem (BVP) for planar Hamiltonian systems. Green's function that is needed for representing the solutions is obtained and its properties are listed. The uniqueness of solutions is connected to a Lyapunov type inequality for the corresponding homogeneous BVP.

scholarly journals A new general fractional-order derivative with Rabotnov fractional-exponential kernel

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3711-3718 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Minvydas Ragulskis ◽  
Thiab Taha
Keyword(s):  
Fractional Order ◽  
Physical Models ◽  
Order Derivative ◽  
Mathematical Approach ◽  
Liouville Type ◽  
Derivative Operator ◽  
Fractional Order Derivative ◽  
Fractional Exponential Function ◽  
Complex Phenomena ◽  
First Time

In this article, a general fractional-order derivative of the Riemann-Liouville type with the non-singular kernel involving the Rabotnov fractional-exponential function is addressed for the first time. A new general fractional-order derivative model for the anomalous diffusion is discussed in detail. The general fractional-order derivative operator formula is as a novel and mathematical approach proposed to give the generalized presentation of the physical models in complex phenomena with power law.

scholarly journals On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Multipoint Boundary ◽  
Liouville Fractional Derivative ◽  
The Right ◽  
Multipoint Boundary Value Problem

We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusionD0+αut+Ft,ut,u′t∋0,0<t<+∞,u0=u′0=0,Dα-1u+∞-∑i=1m-2‍βiuξi=0, whereD0+αis the standard Riemann-Liouville fractional derivative,2<α<3,0<ξ1<ξ2<⋯<ξm-2<+∞, satisfies0<∑i=1m-2‍βiξiα-1<Γ(α),  and  F:[0,+∞)×ℝ×ℝ→𝒫(ℝ)is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

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