Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations

Abstract

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.

Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

“…Proof. To begin the proof, we will transform the problem (2) and (3) into a fixed point problem Au(t) = u(t) (see [21][22][23][24][25]33]), with…”

“…Techniques of decomposition, homotopy, and variation were used to comprehensively analyze the mathematical models [15][16][17][18]. Currently, many methods such as the residual power series, symmetry, spectral, Fourier transform, similarity, and collocation methods are used to study and manage differential equations in both fractional and classical orders, along with their systems (for more details see [6][7][8][9][10][11][12][17][18][19][20][21][22][23][24][25][26][27][28][29]).…”

Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order

“…The existence and uniqueness of solutions for fractional dierential equations or fractional-order's PDEs have been investigated in recent years. For more on the subject, we refer the reader to the following works [6,7,8,9,10,12,13,14,15,16].…”

Existence of solutions to nonlinear Katugampola fractional differential equations with mixed fractional boundary conditions

“…The main results are stated in Section 3: We prove the lemma giving an equivalent integral form of the considered problem, derive the sufficient conditions for the existence of a solution, and deduce some nonexistence results for some class of linear fractional equations, which are very helpful for other researchers in this field. Furthermore, at the end of the article, we compare the proven theorem with other works 15,16 considering similar boundary value problems.…”