Some families of ordinary and partial fractional differintegral equations

Tu, Shih-Tong; Chyan, Ding-Kuo; Srivástava, H. M.

doi:10.1080/10652460108819319

Cited by 24 publications

(11 citation statements)

References 2 publications

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“…Thus, if we make use of the relationships given by (7.14) in our observations (7.15) to (7.18), we are led fairly easily to the following explicit solutions of the general Jacobi differential equation (7.11): In conclusion, we observe that such general results as Theorems 1 to 3 and their various companions (proven by Tu et al [59]) can be applied similarly in order to derive explicit solutions of many other interesting families of ordinary and partial differential equations.…”

Section: Jacobi's Differential Equationmentioning

confidence: 61%

“…We choose to furnish here the generalizations (and unifications) proposed in one of the latest works on this subject by Tu et al [59] in which references to many earlier related works can be found. We find it to be convenient to begin by recalling the following definition of a fractional differintegral (that is, fractional derivative and fractional integral) of…”

Section: The Gauss Equationmentioning

confidence: 99%

“…Tu et al [59]) including (for example) the classical differential equations listed above [cf. Equations (4.1) to (4.7)].…”

Section: The Gauss Equationmentioning

confidence: 99%

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An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Srivástava¹

2017

Contributions

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A b s t r a c t: The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this paper * is to present a brief elementary and introductory approach to the theory of fractional calculus and its applications especially in developing solutions of certain interesting families of ordinary and partial fractional differintegral equations. Relevant connections of some of the results presented in this lecture with those obtained in many other earlier works on this subject will also be indicated.

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Section: Jacobi's Differential Equationmentioning

confidence: 61%

Section: The Gauss Equationmentioning

confidence: 99%

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An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Srivástava¹

2017

Contributions

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“…Some of the most recent contributions on the subject of particular solutions of linear ordinary and partial fractional differintegral equations are those given by Tu et al [19] who presented unification and generalization of a significantly large number of widely scattered results on this subject. We begin by recalling here one of the main results of Tu et al [19], involving a family of linear ordinary fractional differintegral equations, as Theorem 5 below.…”

Section: Property 1 For a Constant mentioning

confidence: 99%

Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators

Yılmazer

Ozturk

2013

Abstract and Applied Analysis

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“…Some of the most recent studies on the subject of particular solutions of linear ordinary and partial fractional differintegral equations are those given by Tu et al [10] who presented unification and generalization of a significantly large number of widely scattered results on this subject, involving a family of linear ordinary fractional differintegral equations as follows.…”

Section: Lemma 11 (Linearity) Let   F Z and   G Z Be Analytic Amentioning

confidence: 99%

Explicit Solutions of Fractional SchröDinger Equation via Fractional Calculus Operators

Yılmazer¹,

Baş²

2012

IJOPCSM

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Some families of ordinary and partial fractional differintegral equations

Cited by 24 publications

References 2 publications

An Elementary and Introductory Approach to Fractional Calculus and Its Applications

An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators

Explicit Solutions of Fractional SchröDinger Equation via Fractional Calculus Operators

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