Existence results for BVP of a class of Hilfer fractional differential equations

In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional dierential equations involving HilferKatugampola derivative subject to nonlocal fractional integral boundary conditions. The reasoning is mainly based upon properties of Mittag-Leer functions, and xed-point methods such as Banach contraction principle and Krasnoselskii's xed point theorem. Moreover, the generalized Gornwall inequality lemma is used to analyze dierent types of stability. Finally, one example is given to illustrate our theoretical results.

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“…Recently, Gao et al,in [9] established the existence and uniqueness of solutions to the Hilfer nonlocal boundary value problem…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by [6,9], in this paper, we will study Hilfer-Katugampola integral boundary value problems for the following relaxation fractional dierential equations:…”

Section: Introductionmentioning

confidence: 99%

Existence and stability results of relaxation fractional differential equations with Hilfer--Katugampola fractional derivative.

Almalahi

Panchal

2020

Advances in the Theory of Nonlinear Analysis and Its Application

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“…Moreover, they discussed some important qualitative properties of solutions such as existence, uniqueness, and stability results in the following chain [15,18,19,25,28,29,30,31,32,33,34]. Recently Gao et al, in [35] established the existence and uniqueness of solutions to the Hilfer nonlocal boundary value problem…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by [35,36], the objective of this study is to investigate the existence, uniqueness as well as the HU and HUR stabilities of the solutions of the proposed problem involving ψ-Hilfer FD of the form:…”

Section: Introductionmentioning

confidence: 99%

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Almalahi

Panchal

2020

J. Math. Anal. Model.

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In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.

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“…It seems that Hilfer et al [1,34] have initially proposed linear differential equations with the new fractional operator, the Hilfer fractional derivative, and applied operational calculus to solve such simple fractional differential equations. Thereafter, Furati et al [4] In [36], Gao and Yu studied Hilfer integral boundary value problems for the following relaxation fractional differential equations:…”

Section: Introductionmentioning

confidence: 99%

Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions

Gou

2018

Bound Value Probl

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This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of the properties of Hilfer fractional calculus, the theory of propagation families as well as the theory of the measure of noncompactness and fixed point methods, we obtain the existence results of mild solutions for Sobolev-type fractional evolution differential equations involving the Hilfer fractional derivative. Finally, an example is presented to illustrate the main result.

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Existence results for BVP of a class of Hilfer fractional differential equations

Cited by 14 publications

References 19 publications

Existence and stability results of relaxation fractional differential equations with Hilfer--Katugampola fractional derivative.

Existence and stability results of relaxation fractional differential equations with Hilfer--Katugampola fractional derivative.

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions

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