Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

Wahash, Hanan A.; Panchal, Satish K.

doi:10.48185/jmam.v1i1.35

Cited by 17 publications

(12 citation statements)

References 42 publications

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“…On the other hand, there has been much more contemplation paid in developing the theory of existence and uniqueness of positive solutions for nonlinear FDEs, through standard fixed‐point techniques; for details see the literature 17–29 …”

Section: Introductionmentioning

confidence: 99%

Positive solutions for fractional boundary value problems under a generalized fractional operator

Jeelani

Saeed

Abdo

et al. 2021

Math Methods in App Sciences

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The work reported here concerns the study of a generalized nonlinear fractional boundary value problem involving ϑ‐fractional derivative in the Riemann–Liouville sense. The existence and uniqueness of positive solutions to the problem at hand are proved. Our discussion relies on the properties of Green's function, the upper and lower solutions method, and the classical fixed point theorems in a cone. Moreover, building upper and lower control functions has an effective role in the analysis. Some examples are given to justify the validity of theoretical results.

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Section: Introductionmentioning

confidence: 99%

Positive solutions for fractional boundary value problems under a generalized fractional operator

Jeelani

Saeed

Abdo

et al. 2021

Math Methods in App Sciences

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“…To get acquainted with some previous research works done based on φ-CF operators so far, we refer to a paper published by Wahash et al [15]. In that paper, Wahash et al designed a generalized φ-fractional differential equation with a simple integral condition as…”

Section: Introductionmentioning

confidence: 99%

Fixed Point and Endpoint Theories for Two Hybrid Fractional Differential Inclusions with Operators Depending on an Increasing Function

Rezapour

Iqbal

Hussain

et al. 2021

Journal of Function Spaces

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The main concentration of the present research is to explore several theoretical criteria for proving the existence results for the suggested boundary problem. In fact, for the first time, we formulate a new hybrid fractional differential inclusion in the φ -Caputo settings depending on an increasing function φ subject to separated mixed φ -hybrid-integro-derivative boundary conditions. In addition to this, we discuss a special case of the proposed φ -inclusion problem in the non- φ -hybrid structure with the help of the endpoint notion. To confirm the consistency of our findings, two specific numerical examples are provided which simulate both φ -hybrid and non- φ -hybrid cases.

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“…In this work, we consider Hilfer-Katugampola type fractional derivative which interpolates some fractional derivatives such as, Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, see [4,5,6,7,8] and the references therein. On the other hand, some researchers via different types of fractional derivatives studied the existence and stability of Ulam-Hyers, which can be found in [10,11,12,13,14,15,16,17,18]. A pantograph is an important tool employed in electric trains in order to collect electric currents from the overload lines.…”

Section: Introductionmentioning

confidence: 99%

Existence and $\delta $-Approximate solution of implicit fractional pantograph equations in the frame of Hilfer-Katugampola operator

Almalahi

Panchal

2021

J Frac Calc & Nonlinear Sys

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The major goal of this research paper is to investigate the existence and uniqueness of an implicit fractional pantograph equation in the frame of the Hilfer-Katugampola operator on the finite interval $[a,b]$ with mixed nonlocal conditions. Our analysis of the existence and uniqueness of solutions depends on some fixed point theorems such as Banach and Krasnoselskii. Moreover, we discuss the dependence of solutions on mixed nonlocal conditions by means of $\delta $-approximated solution. As an application, we provide an example to illustrate the validity of our results.

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Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

Cited by 17 publications

References 42 publications

Positive solutions for fractional boundary value problems under a generalized fractional operator

Positive solutions for fractional boundary value problems under a generalized fractional operator

Fixed Point and Endpoint Theories for Two Hybrid Fractional Differential Inclusions with Operators Depending on an Increasing Function

Existence and $\delta $-Approximate solution of implicit fractional pantograph equations in the frame of Hilfer-Katugampola operator

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