A Method to solve ordinary fractional differential equations using Elzaki and Sumudu transform

Jadhav, Changdev; Dale, Tanisha; Chinchane, Dr. Vaijanath

doi:10.48185/jfcns.v4i1.757

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…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

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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

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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

Application of fractional differential transform method and Bell polynomial for solving system of fractional delay differential equations

Yadav,

Methi

2024

Partial Differential Equations in Applied Mathematics

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Cancer Modeling by Fractional Derivative Equation and Chemotherapy Stabilizing

Moustafid

2024

Communications in Advanced Mathematical Sciences

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This paper discusses the theme of cancer modeling and the problem of control by treatments. We model the cancer cells growth by fractional derivative equation and we stabilize their concentration by chemotherapy. The considered model will be converted into simple partial derivative equation and associated with a viability problem. We use the set-valued analysis to make viable the converted model by regulation law of regulation map. Applied chemotherapy concentration on cancer cells concentration follows the regulation law.

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A Method to solve ordinary fractional differential equations using Elzaki and Sumudu transform

Cited by 3 publications

References 13 publications

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Application of fractional differential transform method and Bell polynomial for solving system of fractional delay differential equations

Cancer Modeling by Fractional Derivative Equation and Chemotherapy Stabilizing

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