‎The spectral analysis of two classes of third order boundary value problems is investigated‎. ‎For every positive integer $m$ we construct two classes of regular third order boundary value problems with at most $2m+1$‎ ‎eigenvalues‎, ‎counting multiplicity‎. ‎These kinds of finite spectrum results are previously known only for even order boundary value problems‎.

In this paper, we studied the existence results for solutions of a new class fractional boundary value problem in Caputo–Hadamard settings. Moreover, conditions were formulated as mixed multi-order Hadamard integro-derivative conditions. To prove main results, applied two well-known techniques topological degree and fixed point theories. Finally, provide examples to show compatibility our theor...

Nowadays, a number of classical order results are being analyzed in the sense fractional derivatives. In this research work, we discuss two different boundary value problems. first half paper, generalize an integer-order problem into fractional-order and then demonstrate existence uniqueness solution subject to Caputo derivative. First, recall some justify our main with proofs given theorems. W...

This paper investigates the sufficient conditions for existence and uniqueness of a class Riemann-Liouville fractional differential equations variable order with boundary conditions. The problem is converted into constant orders by combining concepts generalized intervals piecewise functions. We derive required ensuring in to utilize Banach fixed point theorem. stability obtained solution Ulam-...

Various scholars have lately employed a wide range of strategies to resolve specific types symmetrical fractional differential equations. This paper introduces new implicit finite difference method with variable-order time-fractional Caputo derivative solve semi-linear initial boundary value problems. Despite its extensive use in other areas, calculus has only recently been applied physics. aim...