Existence of Solution for a Katugampola Fractional Differential Equation Using Coincidence Degree Theory

Satyam Narayan Srivastava; Smita Pati; John R. Graef; Alexander Domoshnitsky; Seshadev Padhi

doi:10.1007/s00009-024-02658-5

Existence of Solution for a Katugampola Fractional Differential Equation Using Coincidence Degree Theory

Satyam Narayan Srivastava, Smita Pati, John R. Graef, Alexander Domoshnitsky, Seshadev Padhi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, the authors study the existence of positive solutions to the fractional boundary value problem at resonance (Formula presented.) where 1<α≤2, and D_a+^α,ρ is a Katugampola fractional derivative, which generalizes the Riemann–Liouville and Hadamard fractional derivatives, and ∫_a^bx(t)dA(t) denotes a Riemann–Stieltjes integral of x with respect to A, where A is a function of bounded variation. Coincidence degree theory is applied to obtain existence results. This appears to be the first work in the literature to deal with a resonant fractional differential equation with a Katugampola fractional derivative. Examples are given to illustrate the application of their results.

Original language	English
Article number	123
Journal	Mediterranean Journal of Mathematics
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s00009-024-02658-5
State	Published - Jun 2024

Keywords

26A33
30A08
34B10
boundary value problem
coincidence degree theory
existence of solution
fractional derivative
Fractional integral
Katugampola derivative

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10.1007/s00009-024-02658-5

Cite this

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title = "Existence of Solution for a Katugampola Fractional Differential Equation Using Coincidence Degree Theory",

abstract = "In this paper, the authors study the existence of positive solutions to the fractional boundary value problem at resonance (Formula presented.) where 1<α≤2, and Da+α,ρ is a Katugampola fractional derivative, which generalizes the Riemann–Liouville and Hadamard fractional derivatives, and ∫abx(t)dA(t) denotes a Riemann–Stieltjes integral of x with respect to A, where A is a function of bounded variation. Coincidence degree theory is applied to obtain existence results. This appears to be the first work in the literature to deal with a resonant fractional differential equation with a Katugampola fractional derivative. Examples are given to illustrate the application of their results.",

keywords = "26A33, 30A08, 34B10, boundary value problem, coincidence degree theory, existence of solution, fractional derivative, Fractional integral, Katugampola derivative",

author = "Srivastava, {Satyam Narayan} and Smita Pati and Graef, {John R.} and Alexander Domoshnitsky and Seshadev Padhi",

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AU - Graef, John R.

AU - Domoshnitsky, Alexander

AU - Padhi, Seshadev

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AB - In this paper, the authors study the existence of positive solutions to the fractional boundary value problem at resonance (Formula presented.) where 1<α≤2, and Da+α,ρ is a Katugampola fractional derivative, which generalizes the Riemann–Liouville and Hadamard fractional derivatives, and ∫abx(t)dA(t) denotes a Riemann–Stieltjes integral of x with respect to A, where A is a function of bounded variation. Coincidence degree theory is applied to obtain existence results. This appears to be the first work in the literature to deal with a resonant fractional differential equation with a Katugampola fractional derivative. Examples are given to illustrate the application of their results.

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Existence of Solution for a Katugampola Fractional Differential Equation Using Coincidence Degree Theory

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Keywords

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