Existence and Uniqueness of Solution of Nonlinear Fractional Differential Equations Involving k-Riemann-Liouville Derivative | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 2, 2025, Pages 1-10 PDF (213.5 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.338965.1145 | ||
| Author | ||
| Jagdish A Nanware* | ||
| Dept. of Mathematics,Shrikrishna Mahavidyalaya, Gunjoti, Dist.Dharashiv (M.S) INDIA | ||
| Abstract | ||
| The present study deals with the existence and uniqueness of solution of nonlinear fractional differential equations involving $k$-Riemann-Liouville fractional derivative with boundary conditions. Green's function and Banach contraction principle approach is used to prove solution of nonlinear fractional differential equations involving $k$-Riemann-Liouville fractional derivative with boundary conditions . Fractional differential equation with boundary conditions is reduced to the problem of Volterra integral equations. The equivalence of solution of fractional differential equations involving $k$-Riemann-Liouville fractional derivative with boundary conditions and Volterra integral equations is also proved. The properties of $k$-gamma functions , $k$-beta functions and $k-$ Riemann Liouville fractional deirvatives are considered. The Green's function is obtained to prove the existence and uniqueness of solution of the nonlinear boundary value problem involving $k-$ Riemann Liouville fractional deirvatives. Some properties of the Green's theorem for the existence and uniqueness of solution of nonlinear fractional differential equations involving $k$-Riemann-Liouville derivative with boundary conditions are considered. | ||
| Keywords | ||
| k-Riemann-Liouville fractional derivative; Green's function; Existence and uniqueness; Banach contraction principle | ||
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