Solvability of Fractional Differential Inclusion with a Generalized Caputo Derivative

This paper is devoted to the investigation of a kind of generalized Caputo semilinear fractional differential inclusions with deviated-advanced nonlocal conditions. Solvability of the problem is established by means of the Leray-Schauder’s alternative approach with the help of the Lagrange mean-value classical theorem. Finally, some examples are given to delineate the efficient of theoretical results.

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Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses

Filomat ◽

10.2298/fil1917499l ◽

2019 ◽

Vol 33 (17) ◽

pp. 5499-5510 ◽

Cited By ~ 2

Author(s):

Danfeng Luo ◽

Zhiguo Luo

Keyword(s):

Differential Inclusions ◽

Existence Of Solutions ◽

Mean Value ◽

Mean Value Theorem ◽

Fractional Differential Inclusions ◽

Initial Value ◽

Generalized Gronwall Inequality ◽

Nonlinear Alternative ◽

Fractional Differential ◽

Theoretical Results

In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

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Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions

Archivum Mathematicum ◽

10.5817/am2021-5-285 ◽

2021 ◽

pp. 285-297

Author(s):

Ahmed Zahed ◽

Samira Hamani ◽

John R. Graef

Keyword(s):

Boundary Value Problems ◽

Differential Inclusions ◽

Boundary Value ◽

Nonlocal Conditions ◽

Fractional Differential Inclusions ◽

Fractional Differential

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Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2019.4.2 ◽

2019 ◽

Vol 24 (4) ◽

Author(s):

Alka Chadha ◽

Rathinasamy Sakthivel ◽

Swaroop Nandan Bora

Keyword(s):

Differential Inclusions ◽

Approximate Controllability ◽

Measure Of Noncompactness ◽

Nonlocal Conditions ◽

Sufficient Conditions ◽

Fractional Differential Inclusions ◽

Multivalued Maps ◽

Nonlinear Differential Inclusions ◽

Approximately Controllable ◽

Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.

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On generalized boundary value problems for a class of fractional differential inclusions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2017-0075 ◽

2017 ◽

Vol 20 (6) ◽

Cited By ~ 3

Author(s):

Irene Benedetti ◽

Valeri Obukhovskii ◽

Valentina Taddei

Keyword(s):

Differential Inclusions ◽

Nonlinear Term ◽

Reflexive Banach Space ◽

Mild Solutions ◽

Linear Part ◽

Fractional Differential Inclusions ◽

Local Conditions ◽

Non Local ◽

Fractional Differential ◽

Theoretical Results

AbstractWe prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

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

Journal of Function Spaces ◽

10.1155/2015/651359 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Irene Benedetti ◽

Valeri Obukhovskii ◽

Valentina Taddei

Keyword(s):

Banach Space ◽

Differential Inclusion ◽

Differential Inclusions ◽

Nonlinear Term ◽

Reflexive Banach Space ◽

Nonlocal Conditions ◽

Existence Results ◽

Fractional Differential ◽

Partial Differential Inclusion ◽

Generalized Boundary Condition

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

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Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition

Advances in Difference Equations ◽

10.1186/s13662-021-03397-7 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Adel Lachouri ◽

Mohammed S. Abdo ◽

Abdelouaheb Ardjouni ◽

Bahaaeldin Abdalla ◽

Thabet Abdeljawad

Keyword(s):

Differential Inclusions ◽

Fractional Integral ◽

Fixed Point Theorems ◽

Existence Of Solutions ◽

Integral Boundary Conditions ◽

Fractional Differential Inclusions ◽

Hilfer Fractional Derivative ◽

Integral Boundary ◽

Fractional Differential ◽

Theoretical Results

AbstractIn this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

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