Application of Double Shehu Transforms to Caputo Fractional Partial Differential
Equations

Alfaqeih, Suliman; Bakıcıerler, Gizel; Mısırlı, Emine

doi:10.52280/pujm.2022.540101

Cited by 4 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, finding analytic solutions for these equations is often challenging, and several efficient methods have been proposed to solve them. These methods include the Elzaki and Sumudu transform (10) , inverse fractional Shehu transform (11) , double Shehu transform (12) , Unified predictor-corrector method (13) , Adomian Decomposition Method (14) , Fractional Decomposition Method (15) , and many others. Bachir et al (16) discussed the existence and stability of solutions for a class of Hilfer-Hadamard FDEs.…”

Section: Introductionmentioning

confidence: 99%

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Chanchlani,

Manohar,

Sharma

et al. 2024

IJST

View full text Add to dashboard Cite

Objectives: The aim is to establish prerequisite properties for the Hilfer-Hadamard fractional derivatives and address boundary value problems related to fractional polar Laplace and fractional Sturm-Liouville equations involving Hilfer-Hadamard fractional derivatives. Methods: Existing definitions and findings are utilized to obtain the properties for fractional derivatives, and the Adomian decomposition method is employed to solve the fractional differential equations. Findings: Validity conditions for the law of exponents are determined, and the study investigates the fractional differential equations and their corresponding solutions, possessing the capacity to replace the traditional polar Laplace and Sturm-Liouville boundary value problems to effectively represent real-world phenomena. Novelty: The study introduces the substitution of two consecutively operated Hilfer-Hadamard fractional derivatives with a corresponding single Hilfer-Hadamard fractional derivative using the law of exponents. Additionally, the polar Laplace and Sturm-Liouville boundary value problems are extended to their respective fractional counterparts, expressed in a concise format using HilferHadamard fractional derivatives. Keywords: Adomian decomposition method, Hilfer-Hadamard fractional derivative, Fractional polar Laplace equation, Fractional Sturm-Liouville boundary value problem

show abstract

Section: Introductionmentioning

confidence: 99%

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Chanchlani,

Manohar,

Sharma

et al. 2024

IJST

View full text Add to dashboard Cite

show abstract

“…Their properties and theorems are recent studies, attracting the interest of many mathematicians. Therefore, many researchers have studied new formulations, such as Double Laplace Transform, Double Sumudu Transform, others [6][7].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Conformable Double Shehu Transform for Solving Some Fractional Differential Partial Equations

Benattia

Belghaba

2023

J. Sci. Arts

View full text Add to dashboard Cite

In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to double conformable transformation (CDFSHT). Moreover, we are able to prove some theorems and properties related to this work. We apply the double conformable Sehu transform to solve the initial and boundary problems of linear and (non)homogenous conformable fractional partial differential equations (PDEs). The validity and the applicability of the proposed technique are shown by three numerical examples. Mathematica software is used for Euclidean division of polynomials and drawing graphs.

show abstract

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Ahmed,

Elzaki,

Mohamed

2023

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this work, the double Sumudu–Elzaki transform was used for solving fractional-partial differential equations (FPDEs) with starting and boundary conditions. We will use the fractional-order derivative (Caputo’s derivatives) idea. Theorems and facts that are crucial to the newly introduced transform are also discussed and illustrated. By using this newly designed integral transform and its properties, FPDEs can be reduced into algebraic equations. This strategy has the precise answer since it does not need any discrimination, transformation, or limited assumptions. Five further instances were given to support our conclusions. The results showed that the recommended strategy is superb, reliable, and efficient. It is also a simple method for solving specific problems in a number of applied scientific and technical fields.

show abstract

Application of Double Shehu Transforms to Caputo Fractional Partial Differential Equations

Cited by 4 publications

References 20 publications

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Investigation of Conformable Double Shehu Transform for Solving Some Fractional Differential Partial Equations

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Contact Info

Product

Resources

About