Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions

This paper delves into a novel category of nonlocal boundary value problems concerning nonlinear sequential fractional differential equations, coupled with a unique form of generalized Riemann–Liouville fractional differential integral boundary conditions. For single-valued maps, we employ a transfo...

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Bibliographic Details
Published in:Fractal and fractional 2024-08, Vol.8 (8), p.457
Main Authors: Gunasekaran, Nallappan, Manigandan, Murugesan, Vinoth, Seralan, Vadivel, Rajarathinam
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Calculus
Caputo fractional derivative
Differential equations
existence and uniqueness
Fixed points (mathematics)
fixed-point theorem
Fractional calculus
generalized Riemann–Liouville fractional integral
Investigations
nonlocal conditions
Plasma physics
sequential derivatives
Stability
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Summary:This paper delves into a novel category of nonlocal boundary value problems concerning nonlinear sequential fractional differential equations, coupled with a unique form of generalized Riemann–Liouville fractional differential integral boundary conditions. For single-valued maps, we employ a transformation technique to convert the provided system into an equivalent fixed-point problem, which we then address using standard fixed-point theorems. Following this, we evaluate the stability of these solutions utilizing the Ulam–Hyres stability method. To elucidate the derived findings, we present constructed examples.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8080457