On existence of solution to mixed nonlinear fractional integrodifferential equations

Kharat, V. V.; Hasabe, D. R.; Dhaigude, D. B.

doi:10.12988/ams.2017.77221

ams

2017

DOI: 10.12988/ams.2017.77221

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On existence of solution to mixed nonlinear fractional integrodifferential equations

V. V. Kharat¹,

D. R. Hasabe²,

D. B. Dhaigude³

Abstract: In present paper we establish the existence, uniqueness and boundedness of solutions of mixed nonlinear fractional integrodifferential equations using fixed point theorem.Mathematics Subject Classification: 34A12, 34G20, 26A33

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2023

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Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

Akhlaghi,

Tavassoli Kajani,

Allame

2023

Journal of Mathematics

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In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville fractional integral corresponding to this kind of Müntz functions. Then, using the Gauss–Legendre quadrature rule and by employing the roots of Müntz functions as the collocation points, we arrive at a system of algebraic equations. By solving this system, an approximate solution for the fractional-order integro-differential equation is obtained. We also construct an upper bound for the truncation error of Müntz orthogonal functions, and we analyze the error of the proposed collocation method. Numerical examples are included to demonstrate the validity and accuracy of the method.

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Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

Akhlaghi,

Tavassoli Kajani,

Allame

2023

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

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On existence of solution to mixed nonlinear fractional integrodifferential equations

Abstract: In present paper we establish the existence, uniqueness and boundedness of solutions of mixed nonlinear fractional integrodifferential equations using fixed point theorem.Mathematics Subject Classification: 34A12, 34G20, 26A33

Cited by 1 publication

References 3 publications

Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

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