A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

Mohammed, Pshtiwan Othman

doi:10.5539/jmr.v11n4p43

Cited by 14 publications

(15 citation statements)

References 15 publications

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“…In the last fifteen years, the definition of fractional calculus has been more appropriate to describe historical dependence processes than the local limit definitions of integer ordinary differential equations (ODEs) or partial differential equations (PDEs), and has received more and more attention in many mathematical and physical fields, see for details [34][35][36][37][38][39][40][41][42][43][44]. Differential equations of fractional order are more accurate than differential equations of integer order in describing the nature of things and objective laws.…”

Section: Conformable Fractional Operators and μ -Convexitymentioning

confidence: 99%

Some modifications in conformable fractional integral inequalities

et al. 2020

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The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional calculus. This article investigates the Hermite-Hadamard integral inequalities via the notion of-convexity. After that, we introduce the notion of μ-convexity in the context of conformable operators. In view of this, we establish some Hermite-Hadamard integral inequalities (both trapezoidal and midpoint types) and some special case of those inequalities as well. Finally, we present some examples on special means of real numbers. Furthermore, we offer three plot illustrations to clarify the results.

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Section: Conformable Fractional Operators and μ -Convexitymentioning

confidence: 99%

Some modifications in conformable fractional integral inequalities

et al. 2020

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“…Proof: Proof of this theorem is similar to the existence and uniqueness theorem [29,Theorem 3.2], and it is therefore omitted.…”

Section: Theorem 42mentioning

confidence: 99%

“…Moreover, they provided an existence and uniqueness theorem for the solutions by applying the Banach contraction mapping theorem. After that, Mohammed [29] generalized the above work.…”

Section: Introductionmentioning

confidence: 96%

A Correlation Between Solutions of Uncertain Fractional Forward Difference Equations and Their Paths

Srivástava

Mohammed

2020

Front. Phys.

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We consider the comparison theorems for the fractional forward h-difference equations in the context of discrete fractional calculus. Moreover, we consider the existence and uniqueness theorem for the uncertain fractional forward h-difference equations. After that the relations between the solutions for the uncertain fractional forward h-difference equations with symmetrical uncertain variables and their α-paths are established and verified using the comparison theorems and existence and uniqueness theorem. Finally, two examples are provided to illustrate the relationship between the solutions.

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“…In recent years, the subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance due mainly to its demonstrated applications in the mathematical modelling of numerous seemingly diverse and widespread real-life problems in the fields of mathematical, physical, engineering and statistical sciences. Such operators of fractionalorder derivatives as (for example) the Riemann-Liouville fractional derivative and the Liouville-Caputo fractional derivative are found to be potentially useful in the mathematical modelling of many of these problems (see, for example, [1][2][3][4][5][6][7]).…”

Section: Introductionmentioning

confidence: 99%

Some Higher-Degree Lacunary Fractional Splines in the Approximation of Fractional Differential Equations

et al. 2021

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In this article, we begin by introducing two classes of lacunary fractional spline functions by using the Liouville–Caputo fractional Taylor expansion. We then introduce a new higher-order lacunary fractional spline method. We not only derive the existence and uniqueness of the method, but we also provide the error bounds for approximating the unique positive solution. As applications of our fundamental findings, we offer some Liouville–Caputo fractional differential equations (FDEs) to illustrate the practicability and effectiveness of the proposed method. Several recent developments on the the theory and applications of FDEs in (for example) real-life situations are also indicated.

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A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

Cited by 14 publications

References 15 publications

Some modifications in conformable fractional integral inequalities

Some modifications in conformable fractional integral inequalities

A Correlation Between Solutions of Uncertain Fractional Forward Difference Equations and Their Paths

Some Higher-Degree Lacunary Fractional Splines in the Approximation of Fractional Differential Equations

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