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New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative

Yacine Arioua, Maria Titraoui (2019)

Communications in Mathematics

In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness...

New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions.

Feng, Meiqiang, Zhang, Xuemei, Ge, Weigao (2011)

Boundary Value Problems [electronic only]

New existence results for nonlinear fractional differential equations with three-point integral boundary conditions.

Ahmad, Bashir, Ntouyas, Sotiris K., Alsaedi, Ahmed (2011)

Advances in Difference Equations [electronic only]

Nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces

JinRong Wang, Wei Wei (2012)

Annales Polonici Mathematici

This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.

Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces

Djamila Seba (2017)

Mathematica Bohemica

We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.

Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions

Bashir Ahmad, Sotiris K. Ntouyas (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.

Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.

Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion...

Nonlocal boundary value problem for impulsive differential equations of fractional order.

Yang, Liu, Chen, Haibo (2011)

Advances in Difference Equations [electronic only]

Nontrivial solutions for fractional $q$ -difference boundary value problems.

Ferreira, Rui A.C. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Note on a discretization of a linear fractional differential equation

Jan Čermák, Tomáš Kisela (2010)

Mathematica Bohemica

The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

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