Displaying similar documents to “Vector-valued inequalities for the commutators of fractional integrals with rough kernels”

On a partial Hadamard fractional integral inclusion

Aurelian Cernea (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.

Boundary value problems for differential inclusions with fractional order

Mouffak Benchohra, Samira Hamani (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.

Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

Choukri Derbazi, Hadda Hammouche (2021)

Mathematica Bohemica

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We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.

Hybrid fractional integro-differential inclusions

Sotiris K. Ntouyas, Sorasak Laoprasittichok, Jessada Tariboon (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.

Theorems on some families of fractional differential equations and their applications

Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)

Applications of Mathematics

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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...

Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis

Astha Chauhan, Rajan Arora (2019)

Communications in Mathematics

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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation...