On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

Naz, Samaira

doi:10.3906/mat-2007-67

Cited by 18 publications

(13 citation statements)

References 14 publications

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“…This lemma is important to transform the nonlinear boundary value problem (16) into an equivalent fixed-point problem. The main results for the single valued (k, φ)-Hilfer fractional nonlocal boundary value problem (16) are included in Section 3, while the results for the multivalued (k, φ)-Hilfer fractional nonlocal boundary value problem (17) are presented in Section 4. Finally, Section 5 is dedicated to illustrative examples.…”

Section: Hilfer Fractional Boundary Value Problem With Nonlocal Multi...mentioning

confidence: 99%

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Tariboon

Samadi

Ntouyas

2022

Axioms

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In this paper we initiate the study of boundary value problems for fractional differential equations and inclusions involving (k,ϕ)-Hilfer fractional derivative of order in (1,2]. In the single-valued case the existence and uniqueness results are established by using classical fixed-point theorems, such as Banach, Krasnoselskiĭ and Leray-Schauder. In the multivalued case we consider both cases, when the right-hand side has convex or non-convex values. In the first case, we apply the Leray–Schauder nonlinear alternative for multivalued maps, and in the second, the Covit–Nadler fixed-point theorem for multivalued contractions. All results are well illustrated by numerical examples.

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Section: Hilfer Fractional Boundary Value Problem With Nonlocal Multi...mentioning

confidence: 99%

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Tariboon

Samadi

Ntouyas

2022

Axioms

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“…Nowadays, computations of images of k-analogues of special functions under operators of k-fractional calculus have found significant importance and applications by many references (for instance, see [15][16][17][28][29][30][31][32][33][34][35][36][37][38][39][40]).…”

Section: K-fraction Calculus Of the 2 H (Pk)mentioning

confidence: 99%

Certain fractional formulas of the extended k-hypergeometric functions

et al. 2021

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In this article, we aim to investigate various formulae for the $(p,k)$ ( p , k ) -analogues of Gauss hypergeometric functions, including the integral transforms and the operators of fractional calculus. All the outcomes presented here are of general attractiveness and can yield a number of previous works as special cases.

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“…Nowadays, various studies and extensions of k-fractional calculus operators were presented by several researchers (see, for example, [22][23][24][25][26][27][28]).…”

Section: Fractional Calculus Approachmentioning

confidence: 99%

Further Results on the $(p, k) -$ Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators

Hidan

Boulaaras

Cherif

et al. 2021

Mathematical Problems in Engineering

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In a previous article, first and last researchers introduced an extension of the hypergeometric functions which is called “ p , k -extended hypergeometric functions.” Motivated by this work, here, we derive several novel properties for these functions, including integral representations, derivative formula, k-Beta transform, Laplace and inverse Laplace transforms, and operators of fractional calculus. Relevant connections of some of the discussed results here with those presented in earlier references are outlined.

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On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

Cited by 18 publications

References 14 publications

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Certain fractional formulas of the extended k-hypergeometric functions

Further Results on the $(p, k) -$ Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators

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On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

Cited by 18 publications

References 14 publications

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Certain fractional formulas of the extended k-hypergeometric functions

Further Results on the p , k − Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators

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Further Results on the $(p, k) -$ Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators